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Chow motives of genus one fibrations 属一纤维的周动机
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-21 DOI: 10.1007/s00229-024-01557-z
Daiki Kawabe
{"title":"Chow motives of genus one fibrations","authors":"Daiki Kawabe","doi":"10.1007/s00229-024-01557-z","DOIUrl":"https://doi.org/10.1007/s00229-024-01557-z","url":null,"abstract":"<p>Let <span>(f: X rightarrow C)</span> be a genus 1 fibration from a smooth projective surface, i.e. its generic fiber is a regular genus 1 curve. Let <span>(j: J rightarrow C)</span> be the Jacobian fibration of <i>f</i>. In this paper, we prove that the Chow motives of <i>X</i> and <i>J</i> are isomorphic. As an application, combined with our concomitant work on motives of quasi-elliptic fibrations, we prove Kimura finite-dimensionality for smooth projective surfaces not of general type with geometric genus 0. This generalizes Bloch–Kas–Lieberman’s result to arbitrary characteristic.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"8 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886646","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
Rigidity of bach-flat gradient schouten solitons 巴赫平梯度舒顿孤子的刚性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-08 DOI: 10.1007/s00229-024-01542-6
Valter Borges
{"title":"Rigidity of bach-flat gradient schouten solitons","authors":"Valter Borges","doi":"10.1007/s00229-024-01542-6","DOIUrl":"https://doi.org/10.1007/s00229-024-01542-6","url":null,"abstract":"<p>In this paper, we show that complete Bach-flat Schouten solitons with <span>(nge 4)</span> are rigid. When <span>(n=3)</span> we are able to conclude rigidity under a more general condition, namely when the Bach tensor is divergence-free. These results imply rigidity of locally conformally flat Schouten solitons for <span>(nge 3)</span>.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"52 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598514","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
A note on the capacity estimate in metastability for generic configurations 关于一般配置的代谢能力估计的说明
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-04-08 DOI: 10.1007/s00229-024-01555-1
Benny Avelin, Vesa Julin
{"title":"A note on the capacity estimate in metastability for generic configurations","authors":"Benny Avelin, Vesa Julin","doi":"10.1007/s00229-024-01555-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01555-1","url":null,"abstract":"<p>In this paper we further develop the ideas from Geometric Function Theory initially introduced in Avelin et al. (Commun Math Phys 404:401–437, 2023), to derive capacity estimate in metastability for arbitrary configurations. The novelty of this paper is twofold. First, the graph theoretical connection enables us to exactly compute the pre-factor in the capacity. Second, we complete the method from Avelin et al. (Commun Math Phys 404:401–437, 2023) by providing an upper bound using Geometric Function Theory together with Thompson’s principle, avoiding explicit constructions of test functions.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"103 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-04-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140598142","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 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
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