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On the Brauer groups of fibrations 论纤维的布劳尔群
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03487-8
Yanshuai Qin
{"title":"On the Brauer groups of fibrations","authors":"Yanshuai Qin","doi":"10.1007/s00209-024-03487-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03487-8","url":null,"abstract":"<p>Let <span>({mathcal {X}}rightarrow C)</span> be a flat <i>k</i>-morphism between smooth integral varieties over a finitely generated field <i>k</i> such that the generic fiber <i>X</i> is smooth, projective and geometrically connected. Assuming that <i>C</i> is a curve with function field <i>K</i>, we build a relation between the Tate-Shafarevich group of <span>(textrm{Pic}^0_{X/K})</span> and the geometric Brauer groups of <span>({mathcal {X}})</span> and <i>X</i>, generalizing a theorem of Artin and Grothendieck for fibered surfaces to higher relative dimensions.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Intermediate dimensions under self-affine codings 自曲线编码下的中间尺寸
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03490-z
Zhou Feng
{"title":"Intermediate dimensions under self-affine codings","authors":"Zhou Feng","doi":"10.1007/s00209-024-03490-z","DOIUrl":"https://doi.org/10.1007/s00209-024-03490-z","url":null,"abstract":"<p>Intermediate dimensions were recently introduced by Falconer et al. (Math Z 296:813–830, 2020) to interpolate between the Hausdorff and box-counting dimensions. In this paper, we show that for every subset <i>E</i> of the symbolic space, the intermediate dimensions of the projections of <i>E</i> under typical self-affine coding maps are constant and given by formulas in terms of capacities. Moreover, we extend the results to the generalized intermediate dimensions introduced by Banaji (Monatsh Math 202: 465–506, 2023) in several settings, including the orthogonal projections in Euclidean spaces and the images of fractional Brownian motions.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"52 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140811982","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Remarks on the existence of minimal models of log canonical generalized pairs 关于对数典范广义对的最小模型存在性的评论
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-26 DOI: 10.1007/s00209-024-03489-6
Nikolaos Tsakanikas, Lingyao Xie
{"title":"Remarks on the existence of minimal models of log canonical generalized pairs","authors":"Nikolaos Tsakanikas, Lingyao Xie","doi":"10.1007/s00209-024-03489-6","DOIUrl":"https://doi.org/10.1007/s00209-024-03489-6","url":null,"abstract":"<p>Given an NQC log canonical generalized pair <span>((X,B+M))</span> whose underlying variety <i>X</i> is not necessarily <span>(mathbb {Q})</span>-factorial, we show that one may run a <span>((K_X+B+M))</span>-MMP with scaling of an ample divisor which terminates, provided that <span>((X,B+M))</span> has a minimal model in a weaker sense or that <span>(K_X+B+M)</span> is not pseudo-effective. We also prove the existence of minimal models of pseudo-effective NQC log canonical generalized pairs under various additional assumptions, for instance when the boundary contains an ample divisor.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"15 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On multipliers into martingale $$SL^infty $$ spaces for arbitrary filtrations 论任意滤波的马廷格尔 $$SL^infty$ 空间乘数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-21 DOI: 10.1007/s00209-024-03494-9
Anton Tselishchev
{"title":"On multipliers into martingale $$SL^infty $$ spaces for arbitrary filtrations","authors":"Anton Tselishchev","doi":"10.1007/s00209-024-03494-9","DOIUrl":"https://doi.org/10.1007/s00209-024-03494-9","url":null,"abstract":"<p>In this paper we study the following problem: for a given bounded positive function <i>f</i> on a filtered probability space can we find another function (a multiplier) <i>m</i>, <span>(0le mle 1)</span>, such that the function <i>mf</i> is not “too small” but its square function is bounded? We explicitly show how to construct such multipliers for the usual martingale square function and for so-called conditional square function. Besides that, we show that for the usual square function more general statement can be obtained by application of a non-constructive abstract correction theorem by Kislyakov.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"40 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140636576","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bott vanishing for Fano threefolds 法诺三折的底消失
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-20 DOI: 10.1007/s00209-024-03468-x
Burt Totaro
{"title":"Bott vanishing for Fano threefolds","authors":"Burt Totaro","doi":"10.1007/s00209-024-03468-x","DOIUrl":"https://doi.org/10.1007/s00209-024-03468-x","url":null,"abstract":"<p>Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that <span>(H^j(X,Omega ^i_Xotimes L)=0)</span> for <span>(j&gt;0)</span>, <span>(ige 0)</span>, and <i>L</i> ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"208 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140625420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces 黎曼曲面上斯特克洛夫特征值组合的形状优化
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-15 DOI: 10.1007/s00209-024-03481-0
Romain Petrides
{"title":"Shape optimization for combinations of Steklov eigenvalues on Riemannian surfaces","authors":"Romain Petrides","doi":"10.1007/s00209-024-03481-0","DOIUrl":"https://doi.org/10.1007/s00209-024-03481-0","url":null,"abstract":"<p>We prove existence and regularity of metrics which minimize combinations of Steklov eigenvalues over metrics of unit perimeter on a surface with boundary. We show that there are free boundary minimal immersions into ellipsoids parametrized by eigenvalues, such that the coordinate functions are eigenfunctions with respect to the minimal metrics. This work generalizes Fraser–Schoen’s and the author’s maximization for one eigenvalue among metrics of unit perimeter on a surface giving free boundary minimal immersions into balls. We also generalize the previous results of critical metrics for one eigenvalue to any combination of eigenvalues from target balls to target ellipsoids.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"12 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140583274","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Simples in a cotilting heart 纤纤素心，简简单单
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-13 DOI: 10.1007/s00209-024-03464-1
Lidia Angeleri Hügel, Ivo Herzog, Rosanna Laking
{"title":"Simples in a cotilting heart","authors":"Lidia Angeleri Hügel, Ivo Herzog, Rosanna Laking","doi":"10.1007/s00209-024-03464-1","DOIUrl":"https://doi.org/10.1007/s00209-024-03464-1","url":null,"abstract":"<p>Every cotilting module over a ring <i>R</i> induces a t-structure with a Grothendieck heart in the derived category D(Mod-<i>R</i>). We determine the simple objects in this heart and their injective envelopes, combining torsion-theoretic aspects with methods from the model theory of modules and Auslander-Reiten theory.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601958","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Unfolding and injectivity of the Kudla–Millson lift of genus 1 属 1 的库德拉-米尔森提升的展开和注入性
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-12 DOI: 10.1007/s00209-024-03479-8
Riccardo Zuffetti
{"title":"Unfolding and injectivity of the Kudla–Millson lift of genus 1","authors":"Riccardo Zuffetti","doi":"10.1007/s00209-024-03479-8","DOIUrl":"https://doi.org/10.1007/s00209-024-03479-8","url":null,"abstract":"<p>We unfold the theta integrals defining the Kudla–Millson lift of genus 1 associated to even lattices of signature (<i>b</i>, 2), where <span>(b&gt;2)</span>. This enables us to compute the Fourier expansion of such defining integrals and prove the injectivity of the Kudla–Millson lift. Although the latter result has been already proved in [5], our new procedure has the advantage of paving the ground for a strategy to prove the injectivity of the lift also for the cases of general signature and of genus greater than 1.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"55 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140602259","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Locally free Caldero–Chapoton functions via reflections 通过反射的局部自由卡尔德罗-夏波顿函数
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-12 DOI: 10.1007/s00209-024-03483-y
Lang Mou
{"title":"Locally free Caldero–Chapoton functions via reflections","authors":"Lang Mou","doi":"10.1007/s00209-024-03483-y","DOIUrl":"https://doi.org/10.1007/s00209-024-03483-y","url":null,"abstract":"<p>We study the reflections of locally free Caldero–Chapoton functions associated to representations of Geiß–Leclerc–Schröer’s quivers with relations for symmetrizable Cartan matrices. We prove that for rank 2 cluster algebras, non-initial cluster variables are expressed as locally free Caldero–Chapoton functions of locally free indecomposable rigid representations. Our method gives rise to a new proof of the locally free Caldero–Chapoton formulas obtained by Geiß–Leclerc–Schröer in Dynkin cases. For general acyclic skew-symmetrizable cluster algebras, we prove the formula for any non-initial cluster variable obtained by almost sink and source mutations.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"23 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582828","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds 渐近局部复杂双曲流形的渐近严格伪凸 CR 结构
IF 0.8 3区 数学
Mathematische Zeitschrift Pub Date : 2024-04-10 DOI: 10.1007/s00209-024-03473-0
Alan Pinoy
{"title":"Asymptotic strictly pseudoconvex CR structure for asymptotically locally complex hyperbolic manifolds","authors":"Alan Pinoy","doi":"10.1007/s00209-024-03473-0","DOIUrl":"https://doi.org/10.1007/s00209-024-03473-0","url":null,"abstract":"<p>In this paper, we build a compactification by a strictly pseudoconvex CR structure for a complete and non-compact Kähler manifold whose curvature tensor is asymptotic to that of the complex hyperbolic space. To do so, we study in depth the evolution of various geometric objects that are defined on the leaves of some foliation of the complement of a suitable convex subset, called an <i>essential subset</i>, whose leaves are the equidistant hypersurfaces above this latter subset. With a suitable renormalization which is closely related to the anisotropic nature of the ambient geometry, the above mentioned geometric objects converge near infinity, inducing the claimed structure on the boundary at infinity.</p>","PeriodicalId":18278,"journal":{"name":"Mathematische Zeitschrift","volume":"25 1","pages":""},"PeriodicalIF":0.8,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140582858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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