Thaís M. Dalbelo, Daniel Duarte, Maria Aparecida Soares Ruas
{"title":"Nash blowups of 2-generic determinantal varieties in positive characteristic","authors":"Thaís M. Dalbelo, Daniel Duarte, Maria Aparecida Soares Ruas","doi":"arxiv-2409.04688","DOIUrl":null,"url":null,"abstract":"We show that the Nash blowup of 2-generic determinantal varieties over fields\nof positive characteristic is non-singular. We prove this in two steps.\nFirstly, we explicitly describe the toric structure of such varieties.\nSecondly, we show that in this case the combinatorics of Nash blowups are free\nof characteristic. The result then follows from the analogous result in\ncharacteristic zero proved by W. Ebeling and S. M. Gusein-Zade.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-07","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-2409.04688","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We show that the Nash blowup of 2-generic determinantal varieties over fields
of positive characteristic is non-singular. We prove this in two steps.
Firstly, we explicitly describe the toric structure of such varieties.
Secondly, we show that in this case the combinatorics of Nash blowups are free
of characteristic. The result then follows from the analogous result in
characteristic zero proved by W. Ebeling and S. M. Gusein-Zade.
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