投影德利涅-芒福德堆栈上半可对的模空间

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Research Letters Pub Date : 2024-04-03 DOI:10.4310/mrl.2023.v30.n4.a7

Yijie Lin

{"title":"投影德利涅-芒福德堆栈上半可对的模空间","authors":"Yijie Lin","doi":"10.4310/mrl.2023.v30.n4.a7","DOIUrl":null,"url":null,"abstract":"We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective Deligne–Mumford stacks.We study the deformation and obstruction theories of stable pairs, and then prove the existence of virtual fundamental classes for some cases of dimension two and three. This leads to a definition of Pandharipande–Thomas invariants on three-dimensional smooth projective Deligne–Mumford stacks.","PeriodicalId":49857,"journal":{"name":"Mathematical Research Letters","volume":"30 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Moduli spaces of semistable pairs on projective Deligne–Mumford stacks\",\"authors\":\"Yijie Lin\",\"doi\":\"10.4310/mrl.2023.v30.n4.a7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective Deligne–Mumford stacks.We study the deformation and obstruction theories of stable pairs, and then prove the existence of virtual fundamental classes for some cases of dimension two and three. This leads to a definition of Pandharipande–Thomas invariants on three-dimensional smooth projective Deligne–Mumford stacks.\",\"PeriodicalId\":49857,\"journal\":{\"name\":\"Mathematical Research Letters\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Research Letters\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4310/mrl.2023.v30.n4.a7\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Research Letters","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/mrl.2023.v30.n4.a7","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

我们研究了稳定对的变形和阻塞理论，然后证明了二维和三维某些情况下虚基类的存在。我们研究了稳定对的变形和阻塞理论，然后证明了二维和三维某些情况下虚拟基本类的存在。由此，我们给出了三维光滑投影德利尼-芒福堆栈的潘达里潘德-托马斯不变式的定义。

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

Moduli spaces of semistable pairs on projective Deligne–Mumford stacks

We generalize the construction of a moduli space of semistable pairs parametrizing isomorphism classes of morphisms from a fixed coherent sheaf to any sheaf with fixed Hilbert polynomial under a notion of stability to the case of projective Deligne–Mumford stacks.We study the deformation and obstruction theories of stable pairs, and then prove the existence of virtual fundamental classes for some cases of dimension two and three. This leads to a definition of Pandharipande–Thomas invariants on three-dimensional smooth projective Deligne–Mumford stacks.

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

Mathematical Research Letters 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

6.0 months

期刊介绍： Dedicated to publication of complete and important papers of original research in all areas of mathematics. Expository papers and research announcements of exceptional interest are also occasionally published. High standards are applied in evaluating submissions; the entire editorial board must approve the acceptance of any paper.