等变舒伯特类的刚性

arXiv - MATH - Algebraic Geometry Pub Date : 2024-09-17 DOI:arxiv-2409.11387

Anders S. Buch, Pierre-Emmanuel Chaput, Nicolas Perrin

{"title":"等变舒伯特类的刚性","authors":"Anders S. Buch, Pierre-Emmanuel Chaput, Nicolas Perrin","doi":"arxiv-2409.11387","DOIUrl":null,"url":null,"abstract":"We prove that Schubert varieties in flag manifolds are uniquely determined by\ntheir equivariant cohomology classes, as well as a stronger result that\nreplaces Schubert varieties with closures of Bialynicki-Birula cells under\nsuitable conditions. This is used to prove that any two-pointed curve\nneighborhood representing a quantum cohomology product with a Seidel class is a\nSchubert variety.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Rigidity of equivariant Schubert classes\",\"authors\":\"Anders S. Buch, Pierre-Emmanuel Chaput, Nicolas Perrin\",\"doi\":\"arxiv-2409.11387\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that Schubert varieties in flag manifolds are uniquely determined by\\ntheir equivariant cohomology classes, as well as a stronger result that\\nreplaces Schubert varieties with closures of Bialynicki-Birula cells under\\nsuitable conditions. This is used to prove that any two-pointed curve\\nneighborhood representing a quantum cohomology product with a Seidel class is a\\nSchubert variety.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.11387\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.11387","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

我们证明了旗流形中的舒伯特变是由它们的等变同调类唯一决定的，同时还证明了一个更强的结果，即在合适的条件下，舒伯特变与比利亚里尼奇-比鲁拉单元的闭包可以互换。这一结果被用来证明任何代表量子同调积与塞德尔类的两点卷曲邻域都是舒伯特变。

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

Rigidity of equivariant Schubert classes

We prove that Schubert varieties in flag manifolds are uniquely determined by their equivariant cohomology classes, as well as a stronger result that replaces Schubert varieties with closures of Bialynicki-Birula cells under suitable conditions. This is used to prove that any two-pointed curve neighborhood representing a quantum cohomology product with a Seidel class is a Schubert variety.

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

arXiv - MATH - Algebraic Geometry

自引率

0.00%

发文量