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Local vanishing for toric varieties 环状变的局部消失
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-06 DOI: 10.1007/s00229-024-01553-3
Wanchun Shen, Sridhar Venkatesh, Anh Duc Vo
{"title":"Local vanishing for toric varieties","authors":"Wanchun Shen, Sridhar Venkatesh, Anh Duc Vo","doi":"10.1007/s00229-024-01553-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01553-3","url":null,"abstract":"<p>Let <i>X</i> be a toric variety. We establish vanishing (and non-vanishing) results for the sheaves <span>(R^if_*Omega ^p_{tilde{X}}(log E))</span>, where <span>(f: tilde{X} rightarrow X)</span> is a strong log resolution of singularities with reduced exceptional divisor <i>E</i>. These extend the local vanishing theorem for toric varieties in Mustaţă et al. (J. Inst. Math. Jussieu 19(3):801-819, 2020). Our consideration of these sheaves is motivated by the notion of <i>k</i>-rational singularities introduced by Friedman and Laza (Higher Du Bois and higher rational singularities, 2001). In particular, our results lead to criteria for toric varieties to have <i>k</i>-rational singularities, as defined in Shen et al. (On k-Du Bois and k-rational singularities, 2023).\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598141","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}
引用次数: 0
Abelian covers and the second fundamental form 阿贝尔封面和第二基本形式
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-04 DOI: 10.1007/s00229-024-01556-0
Paola Frediani
{"title":"Abelian covers and the second fundamental form","authors":"Paola Frediani","doi":"10.1007/s00229-024-01556-0","DOIUrl":"https://doi.org/10.1007/s00229-024-01556-0","url":null,"abstract":"<p>We give some conditions on a family of abelian covers of <span>({mathbb P}^1)</span> of genus <i>g</i> curves, that ensure that the family yields a subvariety of <span>({mathsf A}_g)</span> which is not totally geodesic, hence it is not Shimura. As a consequence, we show that for any abelian group <i>G</i>, there exists an integer <i>M</i> which only depends on <i>G</i> such that if <span>(g &gt;M)</span>, then the family yields a subvariety of <span>({mathsf A}_g)</span> which is not totally geodesic. We prove then analogous results for families of abelian covers of <span>({tilde{C}}_t rightarrow {mathbb P}^1 = {tilde{C}}_t/{tilde{G}})</span> with an abelian Galois group <span>({tilde{G}})</span> of even order, proving that under some conditions, if <span>(sigma in {tilde{G}})</span> is an involution, the family of Pryms associated with the covers <span>({tilde{C}}_t rightarrow C_t= {tilde{C}}_t/langle sigma rangle )</span> yields a subvariety of <span>({mathsf A}_{p}^{delta })</span> which is not totally geodesic. As a consequence, we show that if <span>({tilde{G}}=(mathbb Z/Nmathbb Z)^m)</span> with <i>N</i> even, and <span>(sigma )</span> is an involution in <span>({tilde{G}})</span>, there exists an integer <i>M</i>(<i>N</i>) which only depends on <i>N</i> such that, if <span>({tilde{g}}= g({tilde{C}}_t) &gt; M(N))</span>, then the subvariety of the Prym locus in <span>({{mathsf A}}^{delta }_{p})</span> induced by any such family is not totally geodesic (hence it is not Shimura).</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"2011 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140601955","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}
引用次数: 0
Quasi-abelian group as automorphism group of Riemann surfaces 作为黎曼曲面自变群的准阿贝尔群
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-03 DOI: 10.1007/s00229-024-01552-4
Rubén A. Hidalgo, Yerika L. Marín Montilla, Saúl Quispe
{"title":"Quasi-abelian group as automorphism group of Riemann surfaces","authors":"Rubén A. Hidalgo, Yerika L. Marín Montilla, Saúl Quispe","doi":"10.1007/s00229-024-01552-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01552-4","url":null,"abstract":"<p>Conformal/anticonformal actions of the quasi-abelian group <span>(QA_{n})</span> of order <span>(2^n)</span>, for <span>(nge 4)</span>, on closed Riemann surfaces, pseudo-real Riemann surfaces and closed Klein surfaces are considered. We obtain several consequences, such as the solution of the minimum genus problem for the <span>(QA_n)</span>-actions, and for each of these actions, we study the topological rigidity action problem. In the case of pseudo-real Riemann surfaces, attention was typically restricted to group actions that admit anticonformal elements. In this paper, we consider two cases: either <span>(QA_n)</span> has anticonformal elements or only contains conformal elements.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"57 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598143","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}
引用次数: 0
Iterated monodromy group of a PCF quadratic non-polynomial map PCF 二次非多项式映射的迭代单色群
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-02 DOI: 10.1007/s00229-024-01549-z
Özlem Ejder, Yasemin Kara, Ekin Ozman
{"title":"Iterated monodromy group of a PCF quadratic non-polynomial map","authors":"Özlem Ejder, Yasemin Kara, Ekin Ozman","doi":"10.1007/s00229-024-01549-z","DOIUrl":"https://doi.org/10.1007/s00229-024-01549-z","url":null,"abstract":"<p>We study the postcritically finite non-polynomial map <span>(f(x)=frac{1}{(x-1)^2})</span> over a number field <i>k</i> and prove various results about the geometric <span>(G^{textrm{geom}}(f))</span> and arithmetic <span>(G^{textrm{arith}}(f))</span> iterated monodromy groups of <i>f</i>. We show that the elements of <span>(G^{textrm{geom}}(f))</span> are the ones in <span>(G^{textrm{arith}}(f))</span> that fix certain roots of unity by assuming a conjecture on the size of <span>(G^{textrm{geom}}_n(f))</span>. Furthermore, we describe exactly for which <span>(a in k)</span> the Arboreal Galois group <span>(G_a(f))</span> and <span>(G^{textrm{arith}}(f))</span> are equal.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"130 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598132","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}
引用次数: 0
Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with $${varepsilon }$$ -range 具有 $${{varepsilon }$$ 范围的 Bakry-Émery-Ricci 曲率下限下的一些函数不等式
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-02 DOI: 10.1007/s00229-024-01537-3
Yasuaki Fujitani
{"title":"Some functional inequalities under lower Bakry–Émery–Ricci curvature bounds with $${varepsilon }$$ -range","authors":"Yasuaki Fujitani","doi":"10.1007/s00229-024-01537-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01537-3","url":null,"abstract":"<p>For <i>n</i>-dimensional weighted Riemannian manifolds, lower <i>m</i>-Bakry–Émery–Ricci curvature bounds with <span>({varepsilon })</span>-range, introduced by Lu-Minguzzi-Ohta (Anal Geom Metr Spaces 10(1):1–30, 2022), integrate constant lower bounds and certain variable lower bounds in terms of weight functions. In this paper, we prove a Cheng type inequality and a local Sobolev inequality under lower <i>m</i>-Bakry–Émery–Ricci curvature bounds with <span>({varepsilon })</span>-range. These generalize those inequalities under constant curvature bounds for <span>(m in (n,infty ))</span> to <span>(min (-infty ,1]cup {infty })</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598138","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}
引用次数: 0
Submanifolds with constant Moebius curvature and flat normal bundle 具有恒定莫比乌斯曲率和平坦法线束的子曲率
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-01 DOI: 10.1007/s00229-024-01536-4
M. S. R. Antas, R. Tojeiro
{"title":"Submanifolds with constant Moebius curvature and flat normal bundle","authors":"M. S. R. Antas, R. Tojeiro","doi":"10.1007/s00229-024-01536-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01536-4","url":null,"abstract":"<p>We classify isometric immersions <span>(f:M^{n}rightarrow mathbb {R}^{n+p})</span>, <span>(n ge 5)</span> and <span>(2p le n)</span>, with constant Moebius curvature and flat normal bundle.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"130 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598131","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}
引用次数: 0
Local Galois representations associated to additive polynomials 与加法多项式相关的局部伽罗瓦表示
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-30 DOI: 10.1007/s00229-024-01550-6
Takahiro Tsushima
{"title":"Local Galois representations associated to additive polynomials","authors":"Takahiro Tsushima","doi":"10.1007/s00229-024-01550-6","DOIUrl":"https://doi.org/10.1007/s00229-024-01550-6","url":null,"abstract":"<p>For an additive polynomial and a positive integer, we define an irreducible smooth representation of a Weil group of a non-archimedean local field. We study several invariants of this representation. We obtain a necessary and sufficient condition for it to be primitive.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598135","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}
引用次数: 0
Desingularization of generic symmetric and generic skew-symmetric determinantal singularities 一般对称和一般偏斜对称行列式奇点的去奇化
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-20 DOI: 10.1007/s00229-024-01544-4
Sabrina Alexandra Gaube, Bernd Schober
{"title":"Desingularization of generic symmetric and generic skew-symmetric determinantal singularities","authors":"Sabrina Alexandra Gaube, Bernd Schober","doi":"10.1007/s00229-024-01544-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01544-4","url":null,"abstract":"<p>We discuss how to resolve generic skew-symmetric and generic symmetric determinantal singularities. The key ingredients are (skew-) symmetry preserving matrix operations in order to deduce an inductive argument.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140203632","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}
引用次数: 0
Weak approximation on Châtelet surfaces 夏特莱曲面上的弱近似
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-18 DOI: 10.1007/s00229-024-01548-0
Masahiro Nakahara, Samuel Roven
{"title":"Weak approximation on Châtelet surfaces","authors":"Masahiro Nakahara, Samuel Roven","doi":"10.1007/s00229-024-01548-0","DOIUrl":"https://doi.org/10.1007/s00229-024-01548-0","url":null,"abstract":"<p>We study weak approximation for Châtelet surfaces over number fields when all singular fibers are defined over rational points. We consider Châtelet surfaces which satisfy weak approximation over every finite extension of the ground field. We prove many of these results by showing that the Brauer–Manin obstruction vanishes, then apply results of Colliot-Thélène, Sansuc, and Swinnerton-Dyer.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"12 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152646","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}
引用次数: 0
Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary 具有紧凑边界的黎曼流形上指数谐函数的柳维尔定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-16 DOI: 10.1007/s00229-024-01543-5
Xinrong Jiang, Jianyi Mao
{"title":"Liouville theorem for exponentially harmonic functions on Riemannian manifolds with compact boundary","authors":"Xinrong Jiang, Jianyi Mao","doi":"10.1007/s00229-024-01543-5","DOIUrl":"https://doi.org/10.1007/s00229-024-01543-5","url":null,"abstract":"<p>In this note, we derive a Yau type gradient estimate for positive exponentially harmonic functions on Riemannian manifolds with compact boundary. As its application, we obtain a Liouville type theorem.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"20 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152738","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}
引用次数: 0
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