Pub Date : 2016-06-28DOI: 10.2422/2036-2145.201408_006
D. Abramovich, B. Fantechi
We give a new approach for relative and degenerate Gromov-Witten invariants, inspired by that ofJun Li but replacing predeformable maps by transversal maps to a twisted target. The main advantage is a significant simplification in the definition of the obstruction theory. We reprove in our language the degeneration formula, extending it to the orbifold case
{"title":"Orbifold thechniques in degeneration formulas","authors":"D. Abramovich, B. Fantechi","doi":"10.2422/2036-2145.201408_006","DOIUrl":"https://doi.org/10.2422/2036-2145.201408_006","url":null,"abstract":"We give a new approach for relative and degenerate Gromov-Witten \u0000invariants, inspired by that ofJun Li but replacing predeformable maps by transversal \u0000maps to a twisted target. The main advantage is a significant simplification in \u0000the definition of the obstruction theory. We reprove in our language the degeneration \u0000formula, extending it to the orbifold case","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"2 1","pages":"519-579"},"PeriodicalIF":1.4,"publicationDate":"2016-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88042494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-02-25DOI: 10.2422/2036-2145.201308_001
V. Bolotnikov, M. Elin, D. Shoikhet
We present necessary and sufficient conditions for the existence and for the uniqueness of an analytic self-mapping of the open unit disk having prescribed non-tangential boundary asymptotics at finitely many preassigned boundary points.
{"title":"Boundary asymptotic expansions of analytic self-mappings of the unit disk","authors":"V. Bolotnikov, M. Elin, D. Shoikhet","doi":"10.2422/2036-2145.201308_001","DOIUrl":"https://doi.org/10.2422/2036-2145.201308_001","url":null,"abstract":"We present necessary and sufficient conditions for the existence and \u0000for the uniqueness of an analytic self-mapping of the open unit disk having prescribed \u0000non-tangential boundary asymptotics at finitely many preassigned boundary \u0000points.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"8 1","pages":"399-433"},"PeriodicalIF":1.4,"publicationDate":"2016-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82914016","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2422/2036-2145.201309_001
E. Carlini, M. Catalisano, A. Geramita
Polito SFX(opens in a new window)| Export | Download | Add to List | More... Annali della Scuola normale superiore di Pisa - Classe di scienze Volume 15, 2016, Pages 69-84 On the Hilbert function of lines union one non-reduced point (Article) Carlini, E.a , Catalisano, M.V.bc , Geramita, A.V.d a Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca Degli Abbruzzi 24, Torino, Italy b DIME Dipartimento di Ingegneria Meccanica Energetica Gestionale E Dei Trasporti, Universita Degli Studi di Genova, Piazzale Kennedy pad. D, Genova, Italy c Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada View additional affiliations View references (18) Abstract In this paper we consider the problem of determining the Hilbert function of schemes XcP which are the generic union of s lines and one m- multiple point. We completely solve this problem for any s and m when n ≥ 4. When n = 3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.
Polito SFX(在新窗中打开)|导出|下载|添加到列表|更多…Carlini, E.a, Catalisano, M.V.bc, Geramita, A.V.d a数学科学学院，都灵理工大学，Corso Duca Degli Abbruzzi 24，都灵，意大利;b DIME Dipartimento di engegneria Meccanica Energetica Gestionale E Dei交通学院，热那亚Degli Studi di Genova, Piazzale Kennedy pad。(18)摘要本文研究了5条直线和1个m-多点的一般并型XcP格式的Hilbert函数的确定问题。当n≥4时，对于任意s和m，我们完全解决了这个问题。当n = 3时，我们发现了几个有缺陷的方案，并推测它们是唯一的。我们在几个例子中证实了这个猜想。
{"title":"On the Hilbert function of lines union one non-reduced point","authors":"E. Carlini, M. Catalisano, A. Geramita","doi":"10.2422/2036-2145.201309_001","DOIUrl":"https://doi.org/10.2422/2036-2145.201309_001","url":null,"abstract":"Polito SFX(opens in a new window)| Export | Download | Add to List | More... Annali della Scuola normale superiore di Pisa - Classe di scienze Volume 15, 2016, Pages 69-84 On the Hilbert function of lines union one non-reduced point (Article) Carlini, E.a , Catalisano, M.V.bc , Geramita, A.V.d a Dipartimento di Scienze Matematiche, Politecnico di Torino, Corso Duca Degli Abbruzzi 24, Torino, Italy b DIME Dipartimento di Ingegneria Meccanica Energetica Gestionale E Dei Trasporti, Universita Degli Studi di Genova, Piazzale Kennedy pad. D, Genova, Italy c Department of Mathematics and Statistics, Queen's University, Kingston, ON, Canada View additional affiliations View references (18) Abstract In this paper we consider the problem of determining the Hilbert function of schemes XcP which are the generic union of s lines and one m- multiple point. We completely solve this problem for any s and m when n ≥ 4. When n = 3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"7 1","pages":"69-84"},"PeriodicalIF":1.4,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87418267","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2422/2036-2145.201307_008
Thibaut Deheuvels
In this paper, we investigate the existence of W1,p-extension operators for a class of bidimensional ramified domains with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the domains have the (E , δ)-property, and the extension results of Jones imply that there exist such extension operators for all 1 6 p 6 1. In the case where the fractal boundary self-intersects, this result does not hold. In this work we construct extension operators for 1 < p < p?, where p? depends only on the dimension of the self-intersection of the boundary. The construction of the extension operators is based on a Haar wavelet decomposition on the fractal part of the boundary. It relies mainly on the self-similar properties of the domain. The result is sharp in the sense that W1,p-extension operators fail to exist when p > p?.
本文研究了一类具有自相似分形边界的二维分支域的W1,p-扩展算子的存在性。当分形边界不存在自接触时，区域具有(E， δ)-性质，Jones的可拓结果表明，对于所有的1 6 p 6 1都存在这样的可拓算子。在分形边界自相交的情况下，这个结果不成立。在这项工作中，我们构造1 < p < p?p在哪里?只依赖于边界自交的维数。扩展算子的构造基于边界分形部分的Haar小波分解。它主要依赖于域的自相似属性。结果是尖锐的，因为当p > p?时，W1,p-扩展算子不存在。
{"title":"Sobolev extension property for tree-shaped domains with self-contacting fractal boundary","authors":"Thibaut Deheuvels","doi":"10.2422/2036-2145.201307_008","DOIUrl":"https://doi.org/10.2422/2036-2145.201307_008","url":null,"abstract":"In this paper, we investigate the existence of W1,p-extension operators for a class of bidimensional ramified domains with a self-similar fractal boundary previously studied by Mandelbrot and Frame. When the fractal boundary has no self-contact, the domains have the (E , δ)-property, and the extension results of Jones imply that there exist such extension operators for all 1 6 p 6 1. In the case where the fractal boundary self-intersects, this result does not hold. In this work we construct extension operators for 1 < p < p?, where p? depends only on the dimension of the self-intersection of the boundary. The construction of the extension operators is based on a Haar wavelet decomposition on the fractal part of the boundary. It relies mainly on the self-similar properties of the domain. The result is sharp in the sense that W1,p-extension operators fail to exist when p > p?.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"9 1","pages":"209-247"},"PeriodicalIF":1.4,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72615541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2016-01-01DOI: 10.2422/2036-2145.201311_008
E. Barletta, S. Dragomir
We study Bergman-harmonic maps between balls 8 : Bn ! BN extending of class either C2 orM1 to the boundary of Bn. For every holomorphic (anti-holomorphic) map 8 : Bn ! BN extending smoothly to the boundary and every smooth homotopy H : 8 ' 9 we prove a Lichnerowicz-type (cf. [28]) result, i.e., we show that E✏ (9) # E✏ (8) + O(✏−n+1). When 8 is proper, Bergman-harmonic, and C2 up to the boundary, the boundary values map % : S2n−1 ! S2N−1 is shown to satisfy a compatibility system similar to the tangential Cauchy-Riemann equations on S2n−1 (and satisfied by the boundary values of any proper holomorphic map). For every weakly Bergman-harmonic map 8 2 W1(Bn,BN ) admitting Sobolev boundary values % 2 M1(S2n−1,BN ) in the sense of [6], the boundary values % are shown to be a weakly subelliptic harmonic map of (S2n−1, ⌘) into (BN , h), provided that 8−1rh stays bounded at the boundary of Bn and % has vanishing weak normal derivatives.
{"title":"Bergman-harmonic maps of balls","authors":"E. Barletta, S. Dragomir","doi":"10.2422/2036-2145.201311_008","DOIUrl":"https://doi.org/10.2422/2036-2145.201311_008","url":null,"abstract":"We study Bergman-harmonic maps between balls 8 : Bn ! BN extending of class either C2 orM1 to the boundary of Bn. For every holomorphic (anti-holomorphic) map 8 : Bn ! BN extending smoothly to the boundary and every smooth homotopy H : 8 ' 9 we prove a Lichnerowicz-type (cf. [28]) result, i.e., we show that E✏ (9) # E✏ (8) + O(✏−n+1). When 8 is proper, Bergman-harmonic, and C2 up to the boundary, the boundary values map % : S2n−1 ! S2N−1 is shown to satisfy a compatibility system similar to the tangential Cauchy-Riemann equations on S2n−1 (and satisfied by the boundary values of any proper holomorphic map). For every weakly Bergman-harmonic map 8 2 W1(Bn,BN ) admitting Sobolev boundary values % 2 M1(S2n−1,BN ) in the sense of [6], the boundary values % are shown to be a weakly subelliptic harmonic map of (S2n−1, ⌘) into (BN , h), provided that 8−1rh stays bounded at the boundary of Bn and % has vanishing weak normal derivatives.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"37 1","pages":"269-307"},"PeriodicalIF":1.4,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78030098","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-07-30DOI: 10.2422/2036-2145.201508_003
Valentino Tosatti, Yuguang Zhang
We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first Chern class.
{"title":"Finite time collapsing of the Kähler-Ricci flow on threefolds","authors":"Valentino Tosatti, Yuguang Zhang","doi":"10.2422/2036-2145.201508_003","DOIUrl":"https://doi.org/10.2422/2036-2145.201508_003","url":null,"abstract":"We show that if on a compact Kahler threefold there is a solution of the Kahler-Ricci flow which encounters a finite time collapsing singularity, then the manifold admits a Fano fibration. Furthermore, if there is finite time extinction then the manifold is Fano and the initial class is a positive multiple of the first Chern class.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"139 1","pages":"105-118"},"PeriodicalIF":1.4,"publicationDate":"2015-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73451392","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-05-18DOI: 10.2422/2036-2145.201506_009
V. Crismale, F. Fidaleo, Y. Lu
We give sufficient conditions ensuring the strong ergodic property of unique mixing for $C^*$-dynamical systems arising from Yang-Baxter-Hecke quantisation. We discuss whether they can be applied to some important cases including monotone, Boson, Fermion and Boolean $C^*$-algebras in a unified version. The monotone and the Boolean cases are treated in full generality, the Bose/Fermi cases being already widely investigated. In fact, on one hand we show that the set of stationary stochastic processes are isomorphic to a segment in both the situations, on the other hand the Boolean processes enjoy the very strong property of unique mixing with respect to the fixed point subalgebra and the monotone ones do not
{"title":"Ergodic theorems in Quantum Probability: an application to the monotone stochastic processes","authors":"V. Crismale, F. Fidaleo, Y. Lu","doi":"10.2422/2036-2145.201506_009","DOIUrl":"https://doi.org/10.2422/2036-2145.201506_009","url":null,"abstract":"We give sufficient conditions ensuring the strong ergodic property of unique mixing for $C^*$-dynamical systems arising from Yang-Baxter-Hecke quantisation. We discuss whether they can be applied to some important cases including monotone, Boson, Fermion and Boolean $C^*$-algebras in a unified version. The monotone and the Boolean cases are treated in full generality, the Bose/Fermi cases being already widely investigated. In fact, on one hand we show that the set of stationary stochastic processes are isomorphic to a segment in both the situations, on the other hand the Boolean processes enjoy the very strong property of unique mixing with respect to the fixed point subalgebra and the monotone ones do not","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"26 1","pages":"113-141"},"PeriodicalIF":1.4,"publicationDate":"2015-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84996108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-03-27DOI: 10.2422/2036-2145.201505_005
L. Meersseman, M. Nicolau
In this paper we deal with the moduli problem for geometric structures on manifolds. We prove an existence theorem of a local moduli space in a very general setting. Then, to show the strength of this result, we apply it to the case of Sasakian and Sasaki-Einstein structures for which until now only partial results were known.
{"title":"Deformations and Moduli of Structures on Manifolds: General Existence Theorem and Application to the Sasakian Case","authors":"L. Meersseman, M. Nicolau","doi":"10.2422/2036-2145.201505_005","DOIUrl":"https://doi.org/10.2422/2036-2145.201505_005","url":null,"abstract":"In this paper we deal with the moduli problem for geometric structures \u0000on manifolds. We prove an existence theorem of a local moduli space in a very \u0000general setting. Then, to show the strength of this result, we apply it to the case of \u0000Sasakian and Sasaki-Einstein structures for which until now only partial results \u0000were known.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"31 1","pages":"19-63"},"PeriodicalIF":1.4,"publicationDate":"2015-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90181276","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.2422/2036-2145.201107_004
M. Nacinovich, E. Porten
Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p0 ϵ M is necessary and sufficient for holomorphic extension of all germs at p0 of CR functions on M to an ambient neighborhood of p0 in X. As an application, we obtain that CR-hypoellipticity implies the existence of global generic embeddings and prove holomorphic extension for a large class of CR manifolds satisfying a higher order Levi pseudoconcavity condition. We also obtain results on the relationship of holomorphic wedge-extension and the C∞-wave front set for CR distributions.
让M CR子流形的一个复杂的多方面的x本文的主要结果是表明CR-hypoellipticity p0ϵM是必要且充分的全纯扩展的细菌在CR p0功能在x M p0附近环境的应用程序中,我们获得CR-hypoellipticity意味着全球通用的嵌入的存在,证明全纯扩展对于一大类CR集合管满足高阶李维pseudoconcavity条件。我们还得到了CR分布的全纯楔形扩展与C∞波前集的关系。
{"title":"C∞-hypoellipticity and extension of CR functions","authors":"M. Nacinovich, E. Porten","doi":"10.2422/2036-2145.201107_004","DOIUrl":"https://doi.org/10.2422/2036-2145.201107_004","url":null,"abstract":"Let M be a CR submanifold of a complex manifold X. The main result of this article is to show that CR-hypoellipticity at p0 ϵ M is necessary and sufficient for holomorphic extension of all germs at p0 of CR functions on M to an ambient neighborhood of p0 in X. As an application, we obtain that CR-hypoellipticity implies the existence of global generic embeddings and prove holomorphic extension for a large class of CR manifolds satisfying a higher order Levi pseudoconcavity condition. We also obtain results on the relationship of holomorphic wedge-extension and the C∞-wave front set for CR distributions.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"18 1","pages":"677-703"},"PeriodicalIF":1.4,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78282056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-01-01DOI: 10.2422/2036-2145.201209_003
J. Langford
In this paper, we compare the solutions of two PDEs with Neumann boundary conditions, one with given initial data and one with cap symmetrized data. We show that the solution with cap symmetrized data is itself cap symmetrized and exhibits larger convex means. As corollaries, we prove comparison results on spheres and hemispheres, and prove a conjecture of B. Kawohl.
{"title":"Symmetrization of Poisson's equation with Neumann Boundary Conditions","authors":"J. Langford","doi":"10.2422/2036-2145.201209_003","DOIUrl":"https://doi.org/10.2422/2036-2145.201209_003","url":null,"abstract":"In this paper, we compare the solutions of two PDEs with Neumann boundary conditions, one with given initial data and one with cap symmetrized data. We show that the solution with cap symmetrized data is itself cap symmetrized and exhibits larger convex means. As corollaries, we prove comparison results on spheres and hemispheres, and prove a conjecture of B. Kawohl.","PeriodicalId":50966,"journal":{"name":"Annali Della Scuola Normale Superiore Di Pisa-Classe Di Scienze","volume":"18 12","pages":"1025-1063"},"PeriodicalIF":1.4,"publicationDate":"2015-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72399090","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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