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Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds 奇异全局 F 分裂 3 折叠的弱秋槻-中野消失定理
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-10 DOI: 10.1007/s00229-023-01529-9
Kenta Sato, Shunsuke Takagi
{"title":"Weak Akizuki–Nakano vanishing theorem for singular globally F-split 3-folds","authors":"Kenta Sato, Shunsuke Takagi","doi":"10.1007/s00229-023-01529-9","DOIUrl":"https://doi.org/10.1007/s00229-023-01529-9","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"78 3","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139440710","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
Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces 乌尔里希束的科斯祖尔特性和德尔佩佐曲面上稳定束的模空间合理性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-09 DOI: 10.1007/s00229-023-01530-2
Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury
{"title":"Koszul property of Ulrich bundles and rationality of moduli spaces of stable bundles on Del Pezzo surfaces","authors":"Purnaprajna Bangere, Jayan Mukherjee, Debaditya Raychaudhury","doi":"10.1007/s00229-023-01530-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01530-2","url":null,"abstract":"<p>Let <span>({mathscr {E}})</span> be a vector bundle on a smooth projective variety <span>(Xsubseteq {mathbb {P}}^N)</span> that is Ulrich with respect to the hyperplane section <i>H</i>. In this article, we study the Koszul property of <span>({mathscr {E}})</span>, the slope-semistability of the <i>k</i>-th iterated syzygy bundle <span>({mathscr {S}}_k({mathscr {E}}))</span> for all <span>(kge 0)</span> and rationality of moduli spaces of slope-stable bundles on Del Pezzo surfaces. As a consequence of our study, we show that if <i>X</i> is a Del Pezzo surface of degree <span>(dge 4)</span>, then any Ulrich bundle <span>({mathscr {E}})</span> satisfies the Koszul property and is slope-semistable. We also show that, for infinitely many Chern characters <span>(textbf{v}=(r,c_1, c_2))</span>, the corresponding moduli spaces of slope-stable bundles <span>({mathfrak {M}}_H(textbf{v}))</span> when non-empty, are rational, and thereby produce new evidences for a conjecture of Costa and Miró-Roig. As a consequence, we show that the iterated syzygy bundles of Ulrich bundles are dense in these moduli spaces.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"11 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139412916","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
Characterizations of Fano type varieties and projective spaces via absolute complexity 通过绝对复杂性确定法诺型变种和投影空间的特征
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-04 DOI: 10.1007/s00229-023-01526-y
Dae-Won Lee
{"title":"Characterizations of Fano type varieties and projective spaces via absolute complexity","authors":"Dae-Won Lee","doi":"10.1007/s00229-023-01526-y","DOIUrl":"https://doi.org/10.1007/s00229-023-01526-y","url":null,"abstract":"<p>In this paper, we obtain several characterizations of varieties of Fano type and projective spaces via absolute complexity. Also, we show that if the absolute complexity of a given pair <span>((X,Delta ))</span> is negative, then the pair <span>((X,Delta ))</span> does not admit any <span>(-(K_X+Delta ))</span>-minimal models.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"79 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139095564","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
On the torsion part in the K-theory of imaginary quadratic fields. 关于虚二次域 K 理论中的扭转部分。
IF 0.5 4区 数学
Manuscripta Mathematica Pub Date : 2024-01-01 Epub Date: 2024-10-09 DOI: 10.1007/s00229-024-01598-4
Vincent Emery
{"title":"On the torsion part in the <i>K</i>-theory of imaginary quadratic fields.","authors":"Vincent Emery","doi":"10.1007/s00229-024-01598-4","DOIUrl":"https://doi.org/10.1007/s00229-024-01598-4","url":null,"abstract":"<p><p>We obtain upper bounds for the torsion in the <i>K</i>-groups of the ring of integers of imaginary quadratic number fields, in terms of their discriminants.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"175 3-4","pages":"897-903"},"PeriodicalIF":0.5,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11543730/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142631369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${overline{{{mathcal {M}}} }}_g$$ 模空间 $${overline{{mathcal {M}}} 上魏尔-彼得森度量的平均标量曲率估计值}}_g$$
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-12-10 DOI: 10.1007/s00229-023-01523-1
Georg Schumacher, Stefano Trapani
{"title":"Estimates for the average scalar curvature of the Weil–Petersson metric on the moduli space $${overline{{{mathcal {M}}} }}_g$$","authors":"Georg Schumacher, Stefano Trapani","doi":"10.1007/s00229-023-01523-1","DOIUrl":"https://doi.org/10.1007/s00229-023-01523-1","url":null,"abstract":"<p>We give a precise estimate for the average scalar curvature of the Weil–Petersson metric on the moduli space <span>({overline{{{mathcal {M}}} }}_g)</span> as <span>(grightarrow infty )</span> up to the order <span>(1/g^2)</span>.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"3 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138561539","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
Zeta function of some Kummer Calabi-Yau 3-folds 一些库默尔 Calabi-Yau 3 折叠的 Zeta 函数
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-12-07 DOI: 10.1007/s00229-023-01524-0
Dominik Burek
{"title":"Zeta function of some Kummer Calabi-Yau 3-folds","authors":"Dominik Burek","doi":"10.1007/s00229-023-01524-0","DOIUrl":"https://doi.org/10.1007/s00229-023-01524-0","url":null,"abstract":"<p>We compute Hodge numbers and zeta function of a Kummer Calabi-Yau 3-folds introduced by M. Andreatta and J. Wiśniewski in [2] and investigated by M. Donten-Bury in [13].\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"43 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138546702","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
Shifting numbers of abelian varieties via bounded t-structures 通过有界t结构的阿贝尔变异数的移位
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-11-27 DOI: 10.1007/s00229-023-01525-z
Yu-Wei Fan
{"title":"Shifting numbers of abelian varieties via bounded t-structures","authors":"Yu-Wei Fan","doi":"10.1007/s00229-023-01525-z","DOIUrl":"https://doi.org/10.1007/s00229-023-01525-z","url":null,"abstract":"<p>The shifting numbers measure the asymptotic amount by which an endofunctor of a triangulated category translates inside the category, and are analogous to Poincaré translation numbers that are widely used in dynamical systems. Motivated by this analogy, Fan–Filip raised the following question: “Do the shifting numbers define a quasimorphism on the group of autoequivalences of a triangulated category?” An affirmative answer was given by Fan–Filip for the bounded derived category of coherent sheaves on an elliptic curve or an abelian surface, via properties of the spaces of Bridgeland stability conditions on these categories. We prove in this article that the question has an affirmative answer for abelian varieties of arbitrary dimensions, generalizing the result of Fan–Filip. One of the key steps is to establish an alternative definition of the shifting numbers via bounded <i>t</i>-structures on triangulated categories. In particular, the full package of a Bridgeland stability condition (a bounded <i>t</i>-structure, and a central charge on a charge lattice) is not necessary for the purpose of computing the shifting numbers.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"23 1-2","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512718","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
Linear hyperelliptic Hodge integrals 线性超椭圆Hodge积分
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-11-27 DOI: 10.1007/s00229-023-01519-x
Adam Afandi
{"title":"Linear hyperelliptic Hodge integrals","authors":"Adam Afandi","doi":"10.1007/s00229-023-01519-x","DOIUrl":"https://doi.org/10.1007/s00229-023-01519-x","url":null,"abstract":"<p>We provide a closed form expression for linear Hodge integrals on the hyperelliptic locus. Specifically, we find a succinct combinatorial formula for all intersection numbers on the hyperelliptic locus with one <span>(lambda )</span>-class, and powers of a <span>(psi )</span>-class pulled back along the branch map. This is achieved by using Atiyah–Bott localization on a stack of stable maps into the orbifold <span>(left[ {mathbb {P}}^1/{mathbb {Z}}_2right] )</span>.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"45 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138542996","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: 3
The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces p-凸超曲面规定曲率方程的Dirichlet问题
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2023-11-17 DOI: 10.1007/s00229-023-01522-2
Weisong Dong
{"title":"The Dirichlet problem for prescribed curvature equations of p-convex hypersurfaces","authors":"Weisong Dong","doi":"10.1007/s00229-023-01522-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01522-2","url":null,"abstract":"<p>In this paper, we study the Dirichlet problem for <i>p</i>-convex hypersurfaces with prescribed curvature. We prove that there exists a graphic hypersurface satisfying the prescribed curvature equation with homogeneous boundary condition. An interior curvature estimate is also obtained.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"18 5-6","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138512722","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
Polyharmonic surfaces in 3-dimensional homogeneous spaces 三维齐次空间中的多谐曲面
4区 数学
Manuscripta Mathematica Pub Date : 2023-11-13 DOI: 10.1007/s00229-023-01520-4
S.  Montaldo, C.  Oniciuc, A.  Ratto
{"title":"Polyharmonic surfaces in 3-dimensional homogeneous spaces","authors":"S.  Montaldo, C.  Oniciuc, A.  Ratto","doi":"10.1007/s00229-023-01520-4","DOIUrl":"https://doi.org/10.1007/s00229-023-01520-4","url":null,"abstract":"Abstract In the first part of this paper we shall classify proper triharmonic isoparametric surfaces in 3-dimensional homogeneous spaces (Bianchi-Cartan-Vranceanu spaces, shortly BCV-spaces). We shall also prove that triharmonic Hopf cylinders are necessarily CMC. In the last section we shall determine a complete classification of CMC r -harmonic Hopf cylinders in BCV-spaces, $$r ge 3$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>r</mml:mi> <mml:mo>≥</mml:mo> <mml:mn>3</mml:mn> </mml:mrow> </mml:math> . This result ensures the existence, for suitable values of r , of an ample family of new examples of r -harmonic surfaces in BCV-spaces.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"39 18","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136281667","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: 1
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