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{"title":"曲线上阿贝尔变异中纤颤的代数近似","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":"{\"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}","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}
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