{"title":"Projective manifolds whose tangent bundle contains a strictly nef subsheaf","authors":"Jie Liu, Wenhao Ou, Xiaokui Yang","doi":"10.1090/jag/807","DOIUrl":null,"url":null,"abstract":"<p>Suppose that <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\n <mml:semantics>\n <mml:mi>X</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is a projective manifold whose tangent bundle <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper T Subscript upper X\">\n <mml:semantics>\n <mml:msub>\n <mml:mi>T</mml:mi>\n <mml:mi>X</mml:mi>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">T_X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> contains a locally free strictly nef subsheaf. We prove that <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\n <mml:semantics>\n <mml:mi>X</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is isomorphic to either a projective space or a projective bundle over a hyperbolic manifold of general type. Moreover, if the fundamental group <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"pi 1 left-parenthesis upper X right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:msub>\n <mml:mi>π<!-- π --></mml:mi>\n <mml:mn>1</mml:mn>\n </mml:msub>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mi>X</mml:mi>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">\\pi _1(X)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is virtually solvable, then <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper X\">\n <mml:semantics>\n <mml:mi>X</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">X</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is isomorphic to a projective space.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"16","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/807","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 16
Abstract
Suppose that XX is a projective manifold whose tangent bundle TXT_X contains a locally free strictly nef subsheaf. We prove that XX is isomorphic to either a projective space or a projective bundle over a hyperbolic manifold of general type. Moreover, if the fundamental group π1(X)\pi _1(X) is virtually solvable, then XX is isomorphic to a projective space.
期刊介绍：
The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology.
This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.
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