仿射线嵌入代数群的唯一性

IF 0.9 1区数学 Q2 MATHEMATICS Journal of Algebraic Geometry Pub Date : 2016-09-07 DOI:10.1090/JAG/725

P. Feller, Immanuel Stampfli

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We prove that two embeddings of the affine line <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C\">\n <mml:semantics>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"double-struck\">C</mml:mi>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">\\mathbb {C}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> into <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\n <mml:semantics>\n <mml:mi>Y</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> are the same up to an automorphism of <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\n <mml:semantics>\n <mml:mi>Y</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> provided that <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper Y\">\n <mml:semantics>\n <mml:mi>Y</mml:mi>\n <mml:annotation encoding=\"application/x-tex\">Y</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is not isomorphic to a product of a torus <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"left-parenthesis double-struck upper C Superscript asterisk Baseline right-parenthesis Superscript k\">\n <mml:semantics>\n <mml:mrow>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:msup>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"double-struck\">C</mml:mi>\n </mml:mrow>\n <mml:mo>∗</mml:mo>\n </mml:msup>\n <mml:msup>\n <mml:mo stretchy=\"false\">)</mml:mo>\n <mml:mi>k</mml:mi>\n </mml:msup>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">(\\mathbb {C}^\\ast )^k</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> and one of the three varieties <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"double-struck upper C cubed\">\n <mml:semantics>\n <mml:msup>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mi mathvariant=\"double-struck\">C</mml:mi>\n </mml:mrow>\n <mml:mn>3</mml:mn>\n </mml:msup>\n <mml:annotation encoding=\"application/x-tex\">\\mathbb {C}^3</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>, <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S upper L 2\">\n <mml:semantics>\n <mml:msub>\n <mml:mi>SL</mml:mi>\n <mml:mn>2</mml:mn>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\operatorname {SL}_2</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>, and <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper P upper S upper L 2\">\n <mml:semantics>\n <mml:msub>\n <mml:mi>PSL</mml:mi>\n <mml:mn>2</mml:mn>\n </mml:msub>\n <mml:annotation encoding=\"application/x-tex\">\\operatorname {PSL}_2</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula>.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2016-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1090/JAG/725","citationCount":"8","resultStr":"{\"title\":\"Uniqueness of embeddings of the affine line into algebraic groups\",\"authors\":\"P. 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引用次数: 8

摘要

设Y Y为复连通仿射代数群的基变。我们证明了仿射线C \mathbb {C}在Y Y中的两个嵌入是相同的，直到Y Y的自同构，条件是Y Y不同构于环面(C∗)k (\mathbb {C}^\ast)^k与三个变体c3 \mathbb {C}^3, SL 2 \operatorname {SL}_2，和PSL 2 \operatorname {PSL}_2。

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Uniqueness of embeddings of the affine line into algebraic groups

Let Y Y be the underlying variety of a complex connected affine algebraic group. We prove that two embeddings of the affine line C \mathbb {C} into Y Y are the same up to an automorphism of Y Y provided that Y Y is not isomorphic to a product of a torus ( C ∗ ) k (\mathbb {C}^\ast )^k and one of the three varieties C 3 \mathbb {C}^3 , SL 2 \operatorname {SL}_2 , and PSL 2 \operatorname {PSL}_2 .

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来源期刊

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

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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