Pub Date : 2023-01-01DOI: 10.4310/ajm.2023.v27.n3.a5
Vladimir Lazić, Joaquín Moraga, Nikolaos Tsakanikas
We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.
证明了对数正则对的特殊终止及其在广义对中的推广。
{"title":"Special termination for log canonical pairs","authors":"Vladimir Lazić, Joaquín Moraga, Nikolaos Tsakanikas","doi":"10.4310/ajm.2023.v27.n3.a5","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n3.a5","url":null,"abstract":"We prove the special termination for log canonical pairs and its generalisation in the context of generalised pairs.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136008746","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 : 2023-01-01DOI: 10.4310/ajm.2023.v27.n1.a1
Chuangxun Cheng
{"title":"On $pi$-divisible $mathcal{O}$-modules over fields of characteristic $p$","authors":"Chuangxun Cheng","doi":"10.4310/ajm.2023.v27.n1.a1","DOIUrl":"https://doi.org/10.4310/ajm.2023.v27.n1.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392032","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 : 2022-07-06DOI: 10.4310/ajm.2021.v25.n5.a6
V. V. Bavula, V. Bekkert, V. Futorny
For the algebra $mathbb{I}_n = K {langle x_1, dotsc, x_n, partial_1, dotsc, partial_n, int_1, dotsc, int_n rangle}$ of polynomial integrodifferential operators over a field $K$ of characteristic zero, a classification of simple weight and generalized weight (left and right) $mathbb{I}_n$‑modules is given. It is proven that the category of weight $mathbb{I}_n$‑modules is semisimple. An explicit description of generalized weight $mathbb{I}_n$‑modules is given and using it a criterion is obtained for the problem of classification of indecomposable generalized weight $mathbb{I}_n$‑modules to be of finite representation type, tame or wild. In the tame case, a classification of indecomposable generalized weight $mathbb{I}_n$‑modules is given. In the wild case ‘natural‘ tame subcategories are considered with explicit description of indecomposable modules. For an arbitrary ring $R$, we introduce the concept of absolutely prime $R$‑module (a nonzero $R$‑module $M$ is absolutely prime if all nonzero subfactors of $M$ have the same annihilator). It is proven that every generalized weight $mathbb{I}_n$‑module is a unique sum of absolutely prime modules. It is also shown that every indecomposable generalized weight $mathbb{I}_n$‑module is equidimensional. A criterion is given for a generalized weight $mathbb{I}_n$‑module to be finitely generated.
{"title":"Explicit description of generalized weight modules of the algebra of polynomial integro-differential operators $mathbb{I}_n$","authors":"V. V. Bavula, V. Bekkert, V. Futorny","doi":"10.4310/ajm.2021.v25.n5.a6","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n5.a6","url":null,"abstract":"For the algebra $mathbb{I}_n = K {langle x_1, dotsc, x_n, partial_1, dotsc, partial_n, int_1, dotsc, int_n rangle}$ of polynomial integrodifferential operators over a field $K$ of characteristic zero, a classification of simple weight and generalized weight (left and right) $mathbb{I}_n$‑modules is given. It is proven that the category of weight $mathbb{I}_n$‑modules is semisimple. An explicit description of generalized weight $mathbb{I}_n$‑modules is given and using it a criterion is obtained for the problem of classification of indecomposable generalized weight $mathbb{I}_n$‑modules to be of finite representation type, tame or wild. In the tame case, a classification of indecomposable generalized weight $mathbb{I}_n$‑modules is given. In the wild case ‘natural‘ tame subcategories are considered with explicit description of indecomposable modules. For an arbitrary ring $R$, we introduce the concept of <i>absolutely prime</i> $R$‑module (a nonzero $R$‑module $M$ is absolutely prime if all nonzero subfactors of $M$ have the same annihilator). It is proven that every generalized weight $mathbb{I}_n$‑module is a unique sum of absolutely prime modules. It is also shown that every indecomposable generalized weight $mathbb{I}_n$‑module is equidimensional. A criterion is given for a generalized weight $mathbb{I}_n$‑module to be finitely generated.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538226","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 : 2022-07-06DOI: 10.4310/ajm.2021.v25.n5.a2
Mingyi Zhang
We give an explicit formula for the Hodge filtration on the $mathscr{D}_X$-module $mathcal{O}_X (*Z) f^{1-alpha}$ associated to the effective $mathbb{Q}$-divisor $D = alpha cdot Z$, where $0 lt alpha leq 1$ and $Z = (f = 0)$ is an irreducible hypersurface defined by $f$, a weighted homogeneous polynomial with an isolated singularity at the origin. In particular this gives a formula for the Hodge ideals of $D$. We deduce a formula for the generating level of the Hodge filtration, as well as further properties of Hodge ideals in this setting. We also extend the main theorem to the case when $f$ is a germ of holomorphic function that is convenient and has non-degenerate Newton boundary.
{"title":"Hodge filtration and Hodge ideals for $mathbb{Q}$-divisors with weighted homogeneous isolated singularities or convenient non-degenerate singularities","authors":"Mingyi Zhang","doi":"10.4310/ajm.2021.v25.n5.a2","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n5.a2","url":null,"abstract":"We give an explicit formula for the Hodge filtration on the $mathscr{D}_X$-module $mathcal{O}_X (*Z) f^{1-alpha}$ associated to the effective $mathbb{Q}$-divisor $D = alpha cdot Z$, where $0 lt alpha leq 1$ and $Z = (f = 0)$ is an irreducible hypersurface defined by $f$, a weighted homogeneous polynomial with an isolated singularity at the origin. In particular this gives a formula for the Hodge ideals of $D$. We deduce a formula for the generating level of the Hodge filtration, as well as further properties of Hodge ideals in this setting. We also extend the main theorem to the case when $f$ is a germ of holomorphic function that is convenient and has non-degenerate Newton boundary.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538191","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 : 2022-07-06DOI: 10.4310/ajm.2021.v25.n5.a5
Dmitri Burago, Dong Chen
We show that given any Liouville direction and flat Finsler torus, one can make a $C^infty$‑small perturbation on an arbitrarily small disc to get a nondense geodesic in the given direction.
{"title":"Finsler perturbation with nondense geodesics with irrational directions","authors":"Dmitri Burago, Dong Chen","doi":"10.4310/ajm.2021.v25.n5.a5","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n5.a5","url":null,"abstract":"We show that given any Liouville direction and flat Finsler torus, one can make a $C^infty$‑small perturbation on an arbitrarily small disc to get a nondense geodesic in the given direction.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538202","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 : 2022-04-18DOI: 10.4310/ajm.2021.v25.n6.a5
Xu Xu, Chao Zheng
The vertex scaling for piecewise linear metrics on polyhedral surfaces was introduced by Luo [18], who proved the local rigidity by establishing a variational principle and conjectured the global rigidity. Luo’s conjecture was solved by Bobenko-Pinkall-Springborn [3], who also introduced the vertex scaling for piecewise hyperbolic metrics and proved its global rigidity. Bobenko-Pinkall-Spingborn’s proof is based on their observation of the connection of vertex scaling and the geometry of polyhedra in 3-dimensional hyperbolic space and the concavity of the volume of ideal and hyper-ideal tetrahedra. In this paper, we give an elementary and short variational proof of the global rigidity of vertex scaling without involving 3-dimensional hyperbolic geometry. The method is based on continuity of eigenvalues of matrices and the extension of convex functions.
{"title":"A new proof for global rigidity of vertex scaling on polyhedral surfaces","authors":"Xu Xu, Chao Zheng","doi":"10.4310/ajm.2021.v25.n6.a5","DOIUrl":"https://doi.org/10.4310/ajm.2021.v25.n6.a5","url":null,"abstract":"The vertex scaling for piecewise linear metrics on polyhedral surfaces was introduced by Luo [18], who proved the local rigidity by establishing a variational principle and conjectured the global rigidity. Luo’s conjecture was solved by Bobenko-Pinkall-Springborn [3], who also introduced the vertex scaling for piecewise hyperbolic metrics and proved its global rigidity. Bobenko-Pinkall-Spingborn’s proof is based on their observation of the connection of vertex scaling and the geometry of polyhedra in 3-dimensional hyperbolic space and the concavity of the volume of ideal and hyper-ideal tetrahedra. In this paper, we give an elementary and short variational proof of the global rigidity of vertex scaling without involving 3-dimensional hyperbolic geometry. The method is based on continuity of eigenvalues of matrices and the extension of convex functions.","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47416504","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 : 2022-01-01DOI: 10.4310/ajm.2022.v26.n4.a1
M. Alim, Florian Beck, Laura Fredrickson
{"title":"Parabolic Higgs bundles, $tt^ast$ connections and opers","authors":"M. Alim, Florian Beck, Laura Fredrickson","doi":"10.4310/ajm.2022.v26.n4.a1","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n4.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391965","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 : 2022-01-01DOI: 10.4310/ajm.2022.v26.n3.a2
Sören Kleine
{"title":"On the Iwasawa invariants of non-cotorsion Selmer groups","authors":"Sören Kleine","doi":"10.4310/ajm.2022.v26.n3.a2","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n3.a2","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70391952","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 : 2022-01-01DOI: 10.4310/ajm.2022.v26.n5.a1
P. Giblin, Graham M. Reeve
{"title":"Contact of circles with surfaces: Answers to a question of Montaldi","authors":"P. Giblin, Graham M. Reeve","doi":"10.4310/ajm.2022.v26.n5.a1","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n5.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392021","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 : 2022-01-01DOI: 10.4310/ajm.2022.v26.n2.a1
M. Jotz
{"title":"Obstructions to representations up to homotopy and ideals","authors":"M. Jotz","doi":"10.4310/ajm.2022.v26.n2.a1","DOIUrl":"https://doi.org/10.4310/ajm.2022.v26.n2.a1","url":null,"abstract":"","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70392338","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：