Pub Date : 2020-11-02DOI: 10.1215/21562261-10607345
T. Fujisawa
We prove that the relative log de Rham cohomology groups of a projective semistable log smooth degeneration admit a natural textit{limiting} mixed Hodge structure. More precisely, we construct a family of increasing filtrations and a family of nilpotent endomorphisms on the relative log de Rham cohomology groups and show that they satisfy a part of good properties of a nilpotnet orbit in several variables.
我们证明了投影半稳定对数光滑退化的相对log-de-Ram上同调群承认一个自然的｛textit｛limiting｝混合Hodge结构。更确切地说，我们在相对log de Rham上同调群上构造了一个增加滤子族和一个幂零自同态族，并证明它们在几个变量中满足幂零网轨道的一部分好性质。
{"title":"Limiting mixed Hodge structures on the relative log de Rham cohomology groups of a projective semistable log smooth degeneration","authors":"T. Fujisawa","doi":"10.1215/21562261-10607345","DOIUrl":"https://doi.org/10.1215/21562261-10607345","url":null,"abstract":"We prove that the relative log de Rham cohomology groups of a projective semistable log smooth degeneration admit a natural textit{limiting} mixed Hodge structure. More precisely, we construct a family of increasing filtrations and a family of nilpotent endomorphisms on the relative log de Rham cohomology groups and show that they satisfy a part of good properties of a nilpotnet orbit in several variables.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42936399","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 : 2020-09-04DOI: 10.1215/21562261-10577928
Annalisa Grossi, C. Onorati, Davide Cesare Veniani
We prove that any symplectic automorphism of finite order on a manifold of type OG6 acts trivially on the Beauville--Bogomolov--Fujiki lattice and that any birational transformation of finite order acts trivially on its discriminant group. Moreover, we classify all possible invariant and coinvariant sublattices.
{"title":"Symplectic birational transformations of finite order on O’Grady’s sixfolds","authors":"Annalisa Grossi, C. Onorati, Davide Cesare Veniani","doi":"10.1215/21562261-10577928","DOIUrl":"https://doi.org/10.1215/21562261-10577928","url":null,"abstract":"We prove that any symplectic automorphism of finite order on a manifold of type OG6 acts trivially on the Beauville--Bogomolov--Fujiki lattice and that any birational transformation of finite order acts trivially on its discriminant group. Moreover, we classify all possible invariant and coinvariant sublattices.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45718202","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 : 2020-09-01DOI: 10.1215/21562261-2019-0073
François Ballaÿ
Résumé On démontre un analogue du théorème de Liouville effectif valable pour des points fermés sur une variété projective définie sur un corps de nombres. Ce résultat est une version effective d’un théorème récent de McKinnon et Roth. Une partie importante de cet article est consacrée à la démonstration d’une version effective d’un cas particulier d’un théorème remarquable de géométrie diophantienne dû à Faltings et Wüstholz. Combiné à de nouvelles comparaisons explicites entre l’évaluation d’une section d’un fibré en droites et une fonction distance donnée, ce résultat entraîne le théorème principal. Nous présentons également une autre approche, en montrant comment rendre effectifs les arguments de McKinnon et Roth. Ces deux points de vue conduisent à des versions distinctes du théorème principal, fournissant des majorations différentes de la hauteur des points satisfaisant une inégalité analogue à celle du théorème de Liouville classique. Abstract We prove an effective analogue of Liouville’s theorem for closed points on an arbitrary projective variety defined over a number field. Our result can be interpreted as an effective version of a recent theorem proved by McKinnon and Roth. A central part of the paper is dedicated to giving an effective proof of a particular case of a powerful theorem in diophantine geometry proved by Faltings and Wüstholz. This result, combined with new explicit comparisons between evaluation of sections of a line bundle and a given distance function, leads to the expected theorem. We also deal with another approach, showing how to make the arguments of McKinnon and Roth effective. These two points of view lead to distinct versions of our main result, giving different upper bounds for the height of points satisfying a Liouville type inequality.
{"title":"Une généralisation du théorème de Liouville effectif pour les variétés projectives","authors":"François Ballaÿ","doi":"10.1215/21562261-2019-0073","DOIUrl":"https://doi.org/10.1215/21562261-2019-0073","url":null,"abstract":"Résumé On démontre un analogue du théorème de Liouville effectif valable pour des points fermés sur une variété projective définie sur un corps de nombres. Ce résultat est une version effective d’un théorème récent de McKinnon et Roth. Une partie importante de cet article est consacrée à la démonstration d’une version effective d’un cas particulier d’un théorème remarquable de géométrie diophantienne dû à Faltings et Wüstholz. Combiné à de nouvelles comparaisons explicites entre l’évaluation d’une section d’un fibré en droites et une fonction distance donnée, ce résultat entraîne le théorème principal. Nous présentons également une autre approche, en montrant comment rendre effectifs les arguments de McKinnon et Roth. Ces deux points de vue conduisent à des versions distinctes du théorème principal, fournissant des majorations différentes de la hauteur des points satisfaisant une inégalité analogue à celle du théorème de Liouville classique. Abstract We prove an effective analogue of Liouville’s theorem for closed points on an arbitrary projective variety defined over a number field. Our result can be interpreted as an effective version of a recent theorem proved by McKinnon and Roth. A central part of the paper is dedicated to giving an effective proof of a particular case of a powerful theorem in diophantine geometry proved by Faltings and Wüstholz. This result, combined with new explicit comparisons between evaluation of sections of a line bundle and a given distance function, leads to the expected theorem. We also deal with another approach, showing how to make the arguments of McKinnon and Roth effective. These two points of view lead to distinct versions of our main result, giving different upper bounds for the height of points satisfying a Liouville type inequality.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47660245","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 : 2020-06-01DOI: 10.1215/21562261-2019-0072
L. Ha
{"title":"Ck-regularity for ∂¯-equations for a class of convex domains of infinite type in C2","authors":"L. Ha","doi":"10.1215/21562261-2019-0072","DOIUrl":"https://doi.org/10.1215/21562261-2019-0072","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":"60 1","pages":"543-559"},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46565774","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 : 2020-06-01DOI: 10.1215/21562261-2019-0043
J. Tan
{"title":"Boundedness of maximal operator for multilinear Calderón–Zygmund operators on products of variable Hardy spaces","authors":"J. Tan","doi":"10.1215/21562261-2019-0043","DOIUrl":"https://doi.org/10.1215/21562261-2019-0043","url":null,"abstract":"","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49535507","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 : 2020-05-15DOI: 10.1215/21562261-2022-0039
U. Frauenfelder
In this paper we introduce a class of Hamilton delay equations which arise as critical points of an action functional motivated by orbit interactions. We show that the kernel of the Hessian at each critical point of the action functional satisfies a uniform bound on its dimension.
{"title":"Nullity bounds for certain Hamiltonian delay equations","authors":"U. Frauenfelder","doi":"10.1215/21562261-2022-0039","DOIUrl":"https://doi.org/10.1215/21562261-2022-0039","url":null,"abstract":"In this paper we introduce a class of Hamilton delay equations which arise as critical points of an action functional motivated by orbit interactions. We show that the kernel of the Hessian at each critical point of the action functional satisfies a uniform bound on its dimension.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47635606","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 : 2020-05-11DOI: 10.1215/21562261-2022-0035
N. Bortolussi, M. Mombelli
For any 0-cell $B$ in a 2-category $Bc$ we introduce the notion of adjoint algebra $adj_B$. This is an algebra in the center of $Bc$. We prove that, if $ca$ is a finite tensor category, this notion applied to the 2-category of $ca$-module categories, coincides with the one introduced by Shimizu [Further results on the structure of (Co)ends in fintite tensor categories}, Appl. Categor. Struct. (2019). this https URL]. As a consequence of this general approach, we obtain new results on the adjoint algebra for tensor categories.
{"title":"The adjoint algebra for 2-categories","authors":"N. Bortolussi, M. Mombelli","doi":"10.1215/21562261-2022-0035","DOIUrl":"https://doi.org/10.1215/21562261-2022-0035","url":null,"abstract":"For any 0-cell $B$ in a 2-category $Bc$ we introduce the notion of adjoint algebra $adj_B$. This is an algebra in the center of $Bc$. We prove that, if $ca$ is a finite tensor category, this notion applied to the 2-category of $ca$-module categories, coincides with the one introduced by Shimizu [Further results on the structure of (Co)ends in fintite tensor categories}, Appl. Categor. Struct. (2019). this https URL]. As a consequence of this general approach, we obtain new results on the adjoint algebra for tensor categories.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2020-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44277328","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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