{"title":"Algebraic approximations of fibrations in abelian varieties over a curve","authors":"Hsueh-Yung Lin","doi":"10.1090/jag/791","DOIUrl":null,"url":null,"abstract":"<p>For every fibration <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f colon upper X right-arrow upper B\">\n <mml:semantics>\n <mml:mrow>\n <mml:mi>f</mml:mi>\n <mml:mo>:</mml:mo>\n <mml:mi>X</mml:mi>\n <mml:mo stretchy=\"false\">→<!-- → --></mml:mo>\n <mml:mi>B</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">f : X \\to B</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> with <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> a compact Kähler manifold, <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper B\">\n <mml:semantics>\n <mml:mi>B</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">B</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> a smooth projective curve, and a general fiber of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\n <mml:semantics>\n <mml:mi>f</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> an abelian variety, we prove that <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"f\">\n <mml:semantics>\n <mml:mi>f</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">f</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> has an algebraic approximation.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2016-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/791","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: 7
Abstract
For every fibration f:X→Bf : X \to B with XX a compact Kähler manifold, BB a smooth projective curve, and a general fiber of ff an abelian variety, we prove that ff has an algebraic approximation.
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.