Gieseker-Petri轨迹的余维2分量

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2020-02-24 DOI:10.1090/jag/780

Margherita Lelli–Chiesa

{"title":"Gieseker-Petri轨迹的余维2分量","authors":"Margherita Lelli–Chiesa","doi":"10.1090/jag/780","DOIUrl":null,"url":null,"abstract":"<p>We show that the Brill-Noether locus <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper M Subscript 18 comma 16 Superscript 3\">\n <mml:semantics>\n <mml:msubsup>\n <mml:mi>M</mml:mi>\n <mml:mrow class=\"MJX-TeXAtom-ORD\">\n <mml:mn>18</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>16</mml:mn>\n </mml:mrow>\n <mml:mn>3</mml:mn>\n </mml:msubsup>\n <mml:annotation encoding=\"application/x-tex\">M^3_{18,16}</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> is an irreducible component of the Gieseker-Petri locus in genus <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"18\">\n <mml:semantics>\n <mml:mn>18</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">18</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> having codimension <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"2\">\n <mml:semantics>\n <mml:mn>2</mml:mn>\n <mml:annotation encoding=\"application/x-tex\">2</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> in the moduli space of curves. This result disproves a conjecture predicting that the Gieseker-Petri locus is always divisorial.</p>","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2020-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A codimension 2 component of the Gieseker-Petri locus\",\"authors\":\"Margherita Lelli–Chiesa\",\"doi\":\"10.1090/jag/780\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We show that the Brill-Noether locus <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper M Subscript 18 comma 16 Superscript 3\\\">\\n <mml:semantics>\\n <mml:msubsup>\\n <mml:mi>M</mml:mi>\\n <mml:mrow class=\\\"MJX-TeXAtom-ORD\\\">\\n <mml:mn>18</mml:mn>\\n <mml:mo>,</mml:mo>\\n <mml:mn>16</mml:mn>\\n </mml:mrow>\\n <mml:mn>3</mml:mn>\\n </mml:msubsup>\\n <mml:annotation encoding=\\\"application/x-tex\\\">M^3_{18,16}</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> is an irreducible component of the Gieseker-Petri locus in genus <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"18\\\">\\n <mml:semantics>\\n <mml:mn>18</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">18</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> having codimension <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"2\\\">\\n <mml:semantics>\\n <mml:mn>2</mml:mn>\\n <mml:annotation encoding=\\\"application/x-tex\\\">2</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> in the moduli space of curves. This result disproves a conjecture predicting that the Gieseker-Petri locus is always divisorial.</p>\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2020-02-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/jag/780\",\"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/780","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: 1

摘要

我们证明了Brill-Noether轨迹M18,163M^3_{18,16}是亏格18 18中Gieseker-Petri轨迹的不可约分量，在曲线的模空间中具有余维数2 2。这个结果推翻了一个猜想，即吉塞克-佩特里轨迹总是整除的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A codimension 2 component of the Gieseker-Petri locus

We show that the Brill-Noether locus M 18 , 16 3 M^3_{18,16} is an irreducible component of the Gieseker-Petri locus in genus 18 18 having codimension 2 2 in the moduli space of curves. This result disproves a conjecture predicting that the Gieseker-Petri locus is always divisorial.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.