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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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Cuspidal components of Siegel modular forms for large discrete series representations of $$textrm{Sp}_4({mathbb {R}})$$ 的倒轴分量的西格尔模形式的大离散级数表示 $$textrm{Sp}_4({mathbb {R}})$$
4区 数学
Manuscripta Mathematica Pub Date : 2023-11-13 DOI: 10.1007/s00229-023-01513-3
Shuji Horinaga, Hiro-aki Narita
{"title":"Cuspidal components of Siegel modular forms for large discrete series representations of $$textrm{Sp}_4({mathbb {R}})$$","authors":"Shuji Horinaga, Hiro-aki Narita","doi":"10.1007/s00229-023-01513-3","DOIUrl":"https://doi.org/10.1007/s00229-023-01513-3","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136282312","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
Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances 后临界有限分形上自相似狄利克雷形式的存在性及其阻力
4区 数学
Manuscripta Mathematica Pub Date : 2023-11-09 DOI: 10.1007/s00229-023-01521-3
Guanhua Liu
{"title":"Existence of self-similar Dirichlet forms on post-critically finite fractals in terms of their resistances","authors":"Guanhua Liu","doi":"10.1007/s00229-023-01521-3","DOIUrl":"https://doi.org/10.1007/s00229-023-01521-3","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135241329","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
On algebraic Chern classes of flat vector bundles 平面向量束的代数Chern类
4区 数学
Manuscripta Mathematica Pub Date : 2023-11-09 DOI: 10.1007/s00229-023-01518-y
Adrian Langer
{"title":"On algebraic Chern classes of flat vector bundles","authors":"Adrian Langer","doi":"10.1007/s00229-023-01518-y","DOIUrl":"https://doi.org/10.1007/s00229-023-01518-y","url":null,"abstract":"Abstract We show that under some assumptions on the monodromy group some combinations of higher Chern classes of a flat vector bundle are torsion in the Chow group. Similar results hold for flat vector bundles that deform to such flat vector bundles (also in case of quasi-projective varieties). The results are motivated by Bloch’s conjecture on Chern classes of flat vector bundles on smooth complex projective varieties but in some cases they give a more precise information. We also study Higgs version of Bloch’s conjecture and analogous problems in the positive characteristic case.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135191536","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
On the rationality of certain Fano threefolds 论法诺的某些合理性
4区 数学
Manuscripta Mathematica Pub Date : 2023-11-06 DOI: 10.1007/s00229-023-01514-2
Ciro Ciliberto
{"title":"On the rationality of certain Fano threefolds","authors":"Ciro Ciliberto","doi":"10.1007/s00229-023-01514-2","DOIUrl":"https://doi.org/10.1007/s00229-023-01514-2","url":null,"abstract":"Abstract In this paper we study the rationality problem for Fano threefolds $$Xsubset {mathbb P}^{p+1}$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>X</mml:mi> <mml:mo>⊂</mml:mo> <mml:msup> <mml:mrow> <mml:mi>P</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> of genus p , that are Gorenstein, with at most canonical singularities. The main results are: (1) a trigonal Fano threefold of genus p is rational as soon as $$pgeqslant 8$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>8</mml:mn> </mml:mrow> </mml:math> (this result has already been obtained in Przyjalkowski et al. (Izv Math 69(2):365–421, 2005), but we give here an independent proof); (2) a non-trigonal Fano threefold of genus $$pgeqslant 7$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>7</mml:mn> </mml:mrow> </mml:math> containing a plane is rational; (3) any Fano threefold of genus $$pgeqslant 17$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:math> is rational; (4) a Fano threefold of genus $$pgeqslant 12$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>⩾</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> </mml:math> containing an ordinary line $$ell $$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mi>ℓ</mml:mi> </mml:math> in its smooth locus is rational.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135584251","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
Boundedness of regular del Pezzo surfaces over imperfect fields 不完全域上正则del Pezzo曲面的有界性
4区 数学
Manuscripta Mathematica Pub Date : 2023-10-30 DOI: 10.1007/s00229-023-01517-z
Hiromu Tanaka
{"title":"Boundedness of regular del Pezzo surfaces over imperfect fields","authors":"Hiromu Tanaka","doi":"10.1007/s00229-023-01517-z","DOIUrl":"https://doi.org/10.1007/s00229-023-01517-z","url":null,"abstract":"Abstract For a regular del Pezzo surface X , we prove that $$|-12K_X|$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mrow> <mml:mo>|</mml:mo> <mml:mo>-</mml:mo> <mml:mn>12</mml:mn> </mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> </mml:msub> <mml:mrow> <mml:mo>|</mml:mo> </mml:mrow> </mml:mrow> </mml:math> is very ample. Furthermore, we also give an explicit upper bound for the volume $$K_X^2$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:msubsup> <mml:mi>K</mml:mi> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> which depends only on $$[k: k^p]$$ <mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"> <mml:mrow> <mml:mo>[</mml:mo> <mml:mi>k</mml:mi> <mml:mo>:</mml:mo> <mml:msup> <mml:mi>k</mml:mi> <mml:mi>p</mml:mi> </mml:msup> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> for the base field k . As a consequence, we obtain the boundedness of geometrically integral regular del Pezzo surfaces.","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136067570","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: 5
Formal ternary laws and Buchstaber’s 2-groups 正式的三元定律和Buchstaber的两个基团
4区 数学
Manuscripta Mathematica Pub Date : 2023-10-30 DOI: 10.1007/s00229-023-01512-4
Jean Fasel, David Coulette, Frédéric Déglise, Jens Hornbostel
{"title":"Formal ternary laws and Buchstaber’s 2-groups","authors":"Jean Fasel, David Coulette, Frédéric Déglise, Jens Hornbostel","doi":"10.1007/s00229-023-01512-4","DOIUrl":"https://doi.org/10.1007/s00229-023-01512-4","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136017914","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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