Pub Date : 2021-07-02DOI: 10.4310/arkiv.2021.v59.n2.a3
A. Beltr'an, A. Fern'andez-P'erez, Hern'an Neciosup
. We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we give an application to the case of a singular real analytic Levi-flat hypersurface. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.
{"title":"Pull-back of singular Levi-flat hypersurfaces","authors":"A. Beltr'an, A. Fern'andez-P'erez, Hern'an Neciosup","doi":"10.4310/arkiv.2021.v59.n2.a3","DOIUrl":"https://doi.org/10.4310/arkiv.2021.v59.n2.a3","url":null,"abstract":". We study singular real analytic Levi-flat subsets invariant by singular holomorphic foliations in complex projective spaces. We give sufficient conditions for a real analytic Levi-flat subset to be the pull-back of a semianalytic Levi-flat hypersurface in a complex projective surface under a rational map or to be the pull-back of a real algebraic curve under a meromorphic function. In particular, we give an application to the case of a singular real analytic Levi-flat hypersurface. Our results improve previous ones due to Lebl and Bretas–Fernández-Pérez–Mol.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-07DOI: 10.4310/arkiv.2023.v61.n1.a9
Sara Maad Sasane, Alexia Papalazarou
We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in $L^2(mathbb R;mathbb R^n)$. In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.
{"title":"Perturbations of embedded eigenvalues for self-adjoint ODE systems","authors":"Sara Maad Sasane, Alexia Papalazarou","doi":"10.4310/arkiv.2023.v61.n1.a9","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n1.a9","url":null,"abstract":"We consider a perturbation problem for embedded eigenvalues of a self-adjoint differential operator in $L^2(mathbb R;mathbb R^n)$. In particular, we study the set of all small perturbations in an appropriate Banach space for which the embedded eigenvalue remains embedded in the continuous spectrum. We show that this set of small perturbations forms a smooth manifold and we specify its co-dimension. Our methods involve the use of exponential dichotomies, their roughness property and Lyapunov-Schmidt reduction.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70394649","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-02DOI: 10.4310/arkiv.2022.v60.n1.a4
A. Geroldinger, M. A. Khadam
We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of r-invertible r-ideals for certain ideal systems r) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetic phenomena with Krull monoids having infinite class group and prime divisors in all classes.
{"title":"On the arithmetic of monoids of ideals","authors":"A. Geroldinger, M. A. Khadam","doi":"10.4310/arkiv.2022.v60.n1.a4","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a4","url":null,"abstract":"We study the algebraic and arithmetic structure of monoids of invertible ideals (more precisely, of r-invertible r-ideals for certain ideal systems r) of Krull and weakly Krull Mori domains. We also investigate monoids of all nonzero ideals of polynomial rings with at least two indeterminates over noetherian domains. Among others, we show that they are not transfer Krull but they share several arithmetic phenomena with Krull monoids having infinite class group and prime divisors in all classes.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393897","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-03DOI: 10.4310/arkiv.2022.v60.n1.a7
T. Nguyen, Xu Wang
. In [15, Remark 4.1], Ohsawa asked whether it is possible to prove Theorem 4.1 and Theorem 0.1 in [15] using the Berndtsson-Lempert method. We shall answer Ohsawa’s question affirmatively in this paper. Our approach also suggests to introduce the Legendre-Fenchel theory and weak psh-geodesics into the Berndtsson-Lempert method.
{"title":"On a remark by Ohsawa related to the Berndtsson–Lempert method for $L^2$-holomorphic extension","authors":"T. Nguyen, Xu Wang","doi":"10.4310/arkiv.2022.v60.n1.a7","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a7","url":null,"abstract":". In [15, Remark 4.1], Ohsawa asked whether it is possible to prove Theorem 4.1 and Theorem 0.1 in [15] using the Berndtsson-Lempert method. We shall answer Ohsawa’s question affirmatively in this paper. Our approach also suggests to introduce the Legendre-Fenchel theory and weak psh-geodesics into the Berndtsson-Lempert method.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48558581","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-28DOI: 10.4310/arkiv.2022.v60.n1.a8
P. Spanos
We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p(n)(v,w) ≤ Cρ, where ρ < 1 is the spectral radius, then for any Floyd function f that satisfies ∑∞ n=1 nf(n) < ∞, the Dirichlet problem with respect to the Floyd boundary is solvable.
{"title":"Remarks on random walks on graphs and the Floyd boundary","authors":"P. Spanos","doi":"10.4310/arkiv.2022.v60.n1.a8","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a8","url":null,"abstract":"We show that for a uniformly irreducible random walk on a graph, with bounded range, there is a Floyd function for which the random walk converges to its corresponding Floyd boundary. Moreover if we add the assumptions, p(n)(v,w) ≤ Cρ, where ρ < 1 is the spectral radius, then for any Floyd function f that satisfies ∑∞ n=1 nf(n) < ∞, the Dirichlet problem with respect to the Floyd boundary is solvable.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393451","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-19DOI: 10.4310/ARKIV.2022.v60.n2.a6
F. Forstnerič
In this paper, we construct open Stein neighbourhoods of compact sets of the form A ∪ K in a complex space, where K is a compact holomorphically convex set, A is a compact complex curve with boundary bA of class C 2 which may intersect K , and the set A ∩ K is O ( A ) -convex.
{"title":"Stein neighbourhoods of bordered complex curves attached to holomorphically convex sets","authors":"F. Forstnerič","doi":"10.4310/ARKIV.2022.v60.n2.a6","DOIUrl":"https://doi.org/10.4310/ARKIV.2022.v60.n2.a6","url":null,"abstract":"In this paper, we construct open Stein neighbourhoods of compact sets of the form A ∪ K in a complex space, where K is a compact holomorphically convex set, A is a compact complex curve with boundary bA of class C 2 which may intersect K , and the set A ∩ K is O ( A ) -convex.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70394179","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-02-11DOI: 10.4310/arkiv.2022.v60.n1.a1
C. O. Alves, S. Bahrouni, M. Carvalho
In this paper we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin [32] combined with some properties of the weak∗ topology.
{"title":"Multiple solutions for two classes of quasilinear problems defined on a nonreflexive Orlicz–Sobolev space","authors":"C. O. Alves, S. Bahrouni, M. Carvalho","doi":"10.4310/arkiv.2022.v60.n1.a1","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a1","url":null,"abstract":"In this paper we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin [32] combined with some properties of the weak∗ topology.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393838","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-07DOI: 10.4310/arkiv.2022.v60.n1.a6
James Macpherson
We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive 2-representations of weakly fiat 2-categories to this environment. We also consider locally finitary 2-categories and 2-representations with a grading, and prove the associated coalgebra 1-morphisms have a homogeneous structure. We use these results to classify simple transitive 2-representations of certain classes of cyclotomic 2-Kac-Moody algebras.
{"title":"Extension of the $2$-representation theory of finitary $2$-categories to locally (graded) finitary $2$-categories","authors":"James Macpherson","doi":"10.4310/arkiv.2022.v60.n1.a6","DOIUrl":"https://doi.org/10.4310/arkiv.2022.v60.n1.a6","url":null,"abstract":"We extend the 2-representation theory of finitary 2-categories to certain 2-categories with infinitely many objects, denoted locally finitary 2-categories, and extend the classical classification results of simple transitive 2-representations of weakly fiat 2-categories to this environment. We also consider locally finitary 2-categories and 2-representations with a grading, and prove the associated coalgebra 1-morphisms have a homogeneous structure. We use these results to classify simple transitive 2-representations of certain classes of cyclotomic 2-Kac-Moody algebras.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-11-27DOI: 10.4310/arkiv.2023.v61.n1.a11
Xiaojun Wu
In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of coherent sheaves. This method also allows us to derive a Riemann-Roch-Grothendieck formula for a projective morphism between smooth complex compact manifolds. In the general case of complex spaces, the Poincar'e and Dolbeault-Grothendieck lemmas are not always valid. For this reason, and to simplify the exposition, we only consider non singular complex spaces. The appendix presents a calculation of integral Bott-Chern cohomology in top degree for a connected compact manifold.
{"title":"Intersection theory and Chern classes in Bott–Chern cohomology","authors":"Xiaojun Wu","doi":"10.4310/arkiv.2023.v61.n1.a11","DOIUrl":"https://doi.org/10.4310/arkiv.2023.v61.n1.a11","url":null,"abstract":"In this article, we investigate an axiomatic approach introduced by Grivaux for the study of rational Bott-Chern cohomology, and use it in that context to define Chern classes of coherent sheaves. This method also allows us to derive a Riemann-Roch-Grothendieck formula for a projective morphism between smooth complex compact manifolds. In the general case of complex spaces, the Poincar'e and Dolbeault-Grothendieck lemmas are not always valid. For this reason, and to simplify the exposition, we only consider non singular complex spaces. The appendix presents a calculation of integral Bott-Chern cohomology in top degree for a connected compact manifold.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393993","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-20DOI: 10.4310/ARKIV.2021.v59.n2.a1
P. Alexandersson, Ezgi Kantarci Ouguz, Svante Linusson
We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. The second family we consider consists of skew shapes, consisting of rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier result by B. Rhoades and later B. Fontaine and J. Kamnitzer. Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in form of a bicyclic sieving phenomenon. One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occur with the same frequency.
{"title":"Promotion and cyclic sieving on families of SSYT","authors":"P. Alexandersson, Ezgi Kantarci Ouguz, Svante Linusson","doi":"10.4310/ARKIV.2021.v59.n2.a1","DOIUrl":"https://doi.org/10.4310/ARKIV.2021.v59.n2.a1","url":null,"abstract":"We examine a few families of semistandard Young tableaux, for which we observe the cyclic sieving phenomenon under promotion. \u0000The first family we consider consists of stretched hook shapes, where we use the cocharge generating polynomial as CSP-polynomial. \u0000The second family we consider consists of skew shapes, consisting of rectangles. Again, the charge generating polynomial together with promotion exhibits the cyclic sieving phenomenon. This generalizes earlier result by B. Rhoades and later B. Fontaine and J. Kamnitzer. \u0000Finally, we consider certain skew ribbons, where promotion behaves in a predictable manner. This result is stated in form of a bicyclic sieving phenomenon. \u0000One of the tools we use is a novel method for computing charge of skew semistandard tableaux, in the case when every number in the tableau occur with the same frequency.","PeriodicalId":55569,"journal":{"name":"Arkiv for Matematik","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70393723","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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