Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202105_058
P. Gille, Laurent Moret-Bailly
: We investigate topological properties of torsors in algebraic geo-metry over adelic rings. Résumé. Nous étudions les propriétés topologiques des torseurs en géométrie algébrique sur des anneaux d’adèles.
{"title":"Fibrés principaux et adèles","authors":"P. Gille, Laurent Moret-Bailly","doi":"10.2422/2036-2145.202105_058","DOIUrl":"https://doi.org/10.2422/2036-2145.202105_058","url":null,"abstract":": We investigate topological properties of torsors in algebraic geo-metry over adelic rings. Résumé. Nous étudions les propriétés topologiques des torseurs en géométrie algébrique sur des anneaux d’adèles.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78300454","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202109_012
M. A. Barja
We prove the equivalence between Clifford-Severi inequalities for good classes of varieties of maximal Albanese dimension and Slope Inequalities for such varieties fibred over curves. This provides a big set of new Slope Inequalities and characterizes the limit cases. It also gives a machinery to automatically obtain other higher dimensional Slope and CliffordSeveri inequalities from inequalities in low dimension. For this, we construct a continuous version of Xiao’s method for irregular fibrations.
{"title":"Slope inequalities for higher dimensional irregular fibrations","authors":"M. A. Barja","doi":"10.2422/2036-2145.202109_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202109_012","url":null,"abstract":"We prove the equivalence between Clifford-Severi inequalities for good classes of varieties of maximal Albanese dimension and Slope Inequalities for such varieties fibred over curves. This provides a big set of new Slope Inequalities and characterizes the limit cases. It also gives a machinery to automatically obtain other higher dimensional Slope and CliffordSeveri inequalities from inequalities in low dimension. For this, we construct a continuous version of Xiao’s method for irregular fibrations.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"18 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73899770","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202105_030
Omar Anza Hafsa, Jean-Philippe Mandallena
{"title":"Gamma-convergence of nonconvex unbounded integrals in Cheeger-Sobolev spaces","authors":"Omar Anza Hafsa, Jean-Philippe Mandallena","doi":"10.2422/2036-2145.202105_030","DOIUrl":"https://doi.org/10.2422/2036-2145.202105_030","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"47 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84765758","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-28DOI: 10.2422/2036-2145.202111_026
S. Dwivedi, E. Loubeau, Henrique N. Sá Earp
{"title":"Harmonic flow of Spin(7)-structures","authors":"S. Dwivedi, E. Loubeau, Henrique N. Sá Earp","doi":"10.2422/2036-2145.202111_026","DOIUrl":"https://doi.org/10.2422/2036-2145.202111_026","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"207 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73004535","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-22DOI: 10.2422/2036-2145.202208_012
Samir Canning, H. Larson
We determine the rational Chow ring of the moduli space $mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n leq 2g+6$. We also show that the Chow ring of the partial compactification $mathcal{I}_{g,n}$, parametrizing $n$-pointed irreducible nodal hyperelliptic curves, is generated by tautological divisors. Along the way, we improve Casnati's result that $mathcal{H}_{g,n}$ is rational for $n leq 2g+8$ to show $mathcal{H}_{g,n}$ is rational for $n leq 3g+5$.
{"title":"The rational Chow rings of moduli spaces of hyperelliptic curves with marked points","authors":"Samir Canning, H. Larson","doi":"10.2422/2036-2145.202208_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_012","url":null,"abstract":"We determine the rational Chow ring of the moduli space $mathcal{H}_{g,n}$ of $n$-pointed smooth hyperelliptic curves of genus $g$ when $n leq 2g+6$. We also show that the Chow ring of the partial compactification $mathcal{I}_{g,n}$, parametrizing $n$-pointed irreducible nodal hyperelliptic curves, is generated by tautological divisors. Along the way, we improve Casnati's result that $mathcal{H}_{g,n}$ is rational for $n leq 2g+8$ to show $mathcal{H}_{g,n}$ is rational for $n leq 3g+5$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"13 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85008495","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-07-13DOI: 10.2422/2036-2145.202208_003
T. Cie'slak, P. Kokocki, W. O.za'nski
We consider solutions of the 2D incompressible Euler equation in the form of $Mgeq 1$ cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are nonsymmetric in the sense that the angles of the individual spirals are not uniformly distributed over the unit circle. Namely, we show that if $M=2$ or $Mgeq 3 $ is an odd integer such that certain non-degeneracy conditions hold, then, for each $n in { 1,2 }$, there exists a logarithmic spiral with $M$ branches of relative angles arbitrarily close to $bartheta_{k} = knpi/M$ for $k=0,1,ldots , M-1$, which include halves of the angles of the Alexander spirals. We show that the non-degeneracy conditions are satisfied if $Min { 2, 3,5,7,9 }$, and that the conditions hold for all odd $M>9$ given a certain gradient matrix is invertible, which appears to be true by numerical computations.
{"title":"Existence of nonsymmetric logarithmic spiral vortex sheet solutions to the 2D Euler equations","authors":"T. Cie'slak, P. Kokocki, W. O.za'nski","doi":"10.2422/2036-2145.202208_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202208_003","url":null,"abstract":"We consider solutions of the 2D incompressible Euler equation in the form of $Mgeq 1$ cocentric logarithmic spirals. We prove the existence of a generic family of spirals that are nonsymmetric in the sense that the angles of the individual spirals are not uniformly distributed over the unit circle. Namely, we show that if $M=2$ or $Mgeq 3 $ is an odd integer such that certain non-degeneracy conditions hold, then, for each $n in { 1,2 }$, there exists a logarithmic spiral with $M$ branches of relative angles arbitrarily close to $bartheta_{k} = knpi/M$ for $k=0,1,ldots , M-1$, which include halves of the angles of the Alexander spirals. We show that the non-degeneracy conditions are satisfied if $Min { 2, 3,5,7,9 }$, and that the conditions hold for all odd $M>9$ given a certain gradient matrix is invertible, which appears to be true by numerical computations.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"27 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82502245","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-19DOI: 10.2422/2036-2145.202302_003
A. Miller
If $n>4$ and $c(theta)$ denotes the set of irreducible constituents of a character $theta$, then $c(chi^k)={rm Irr}(S_n)$ for all nonlinear $chiin {rm Irr}(S_n)$ if and only if $kgeq n-1$.
{"title":"Covering numbers for characters of symmetric groups","authors":"A. Miller","doi":"10.2422/2036-2145.202302_003","DOIUrl":"https://doi.org/10.2422/2036-2145.202302_003","url":null,"abstract":"If $n>4$ and $c(theta)$ denotes the set of irreducible constituents of a character $theta$, then $c(chi^k)={rm Irr}(S_n)$ for all nonlinear $chiin {rm Irr}(S_n)$ if and only if $kgeq n-1$.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89441414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-15DOI: 10.2422/2036-2145.202206_012
Shin-ichi Ohta, Wei Zhao
This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and upper gradients in asymmetric metric spaces, and establish the existence of a curve of maximal slope, which is regarded as a gradient curve in the non-smooth setting. { Introducing} a natural convexity assumption on the potential function, { which is called the $(p,lambda)$-convexity,} we also obtain some regularizing effects on the asymptotic behavior of curves of maximal slope. Applications include several existence results for gradient flows in Finsler manifolds, doubly nonlinear differential evolution equations on { infinite-dimensional Funk spaces}, and heat flow on compact Finsler manifolds.
{"title":"Gradient flows in asymmetric metric spaces","authors":"Shin-ichi Ohta, Wei Zhao","doi":"10.2422/2036-2145.202206_012","DOIUrl":"https://doi.org/10.2422/2036-2145.202206_012","url":null,"abstract":"This paper is devoted to the investigation of gradient flows in asymmetric metric spaces (for example, irreversible Finsler manifolds and Minkowski normed spaces) by means of discrete approximation. We study basic properties of curves and upper gradients in asymmetric metric spaces, and establish the existence of a curve of maximal slope, which is regarded as a gradient curve in the non-smooth setting. { Introducing} a natural convexity assumption on the potential function, { which is called the $(p,lambda)$-convexity,} we also obtain some regularizing effects on the asymptotic behavior of curves of maximal slope. Applications include several existence results for gradient flows in Finsler manifolds, doubly nonlinear differential evolution equations on { infinite-dimensional Funk spaces}, and heat flow on compact Finsler manifolds.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"45 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85343343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-06DOI: 10.2422/2036-2145.202110_007
Elia Brué, Enrico Pasqualetto, Daniele Semola
{"title":"Constancy of the dimension in codimension one and locality of the unit normal on $RCD(K,N)$ spaces","authors":"Elia Brué, Enrico Pasqualetto, Daniele Semola","doi":"10.2422/2036-2145.202110_007","DOIUrl":"https://doi.org/10.2422/2036-2145.202110_007","url":null,"abstract":"","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"11 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72609257","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-06-06DOI: 10.2422/2036-2145.202105_009
Josef Greilhuber, B. Lamel
We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a minimal manifold into such a foliated target is either generically smooth or geometrically highly constrained, and to show generic smoothness of sufficiently regular CR transversal CR maps between pseudoconvex hypersurfaces. As an application, we discuss boundary regularity of proper holomorphic maps into bounded symmetric domains.
{"title":"Regularity of CR maps into uniformly pseudo convex hyper surfaces and applications to proper holomorphic maps","authors":"Josef Greilhuber, B. Lamel","doi":"10.2422/2036-2145.202105_009","DOIUrl":"https://doi.org/10.2422/2036-2145.202105_009","url":null,"abstract":"We study regularity properties of CR maps in positive codimension valued in pseudoconvex manifolds which carry a nontrivial Levi foliation. We introduce an invariant which can be used to deduce that any sufficiently regular CR map from a minimal manifold into such a foliated target is either generically smooth or geometrically highly constrained, and to show generic smoothness of sufficiently regular CR transversal CR maps between pseudoconvex hypersurfaces. As an application, we discuss boundary regularity of proper holomorphic maps into bounded symmetric domains.","PeriodicalId":8132,"journal":{"name":"ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE","volume":"21 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83607133","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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