椭圆稳定映射模空间的两种去广化的比较

Pub Date : 2021-01-01 DOI:10.4134/JKMS.J200163

Hyenho Lho

{"title":"椭圆稳定映射模空间的两种去广化的比较","authors":"Hyenho Lho","doi":"10.4134/JKMS.J200163","DOIUrl":null,"url":null,"abstract":". We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two diﬀerent ways to desingu-larize this space. One is Vakil-Zinger’s desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger’s desingularization.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"COMPARISON OF TWO DESINGULARIZATIONS OF THE MODULI SPACE OF ELLIPTIC STABLE MAPS\",\"authors\":\"Hyenho Lho\",\"doi\":\"10.4134/JKMS.J200163\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two diﬀerent ways to desingu-larize this space. One is Vakil-Zinger’s desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger’s desingularization.\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4134/JKMS.J200163\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4134/JKMS.J200163","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

。研究了椭圆稳定映射到射影空间的模空间的几何性质。椭圆稳定映射的模空间的主成分是奇异的。有两种不同的方式来设计这个空间。一种是Vakil-Zinger去广化，另一种是通过对数稳定映射的模空间去广化。我们的主要结果是证明了这两个空间之间的直接几何关系。对于小于或等于3度的对数稳定映射，我们通过对Vakil-Zinger去广化证明了其模空间的可得性。

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

COMPARISON OF TWO DESINGULARIZATIONS OF THE MODULI SPACE OF ELLIPTIC STABLE MAPS

. We study the geometry of the moduli space of elliptic stable maps to projective space. The main component of the moduli space of elliptic stable maps is singular. There are two diﬀerent ways to desingu-larize this space. One is Vakil-Zinger’s desingularization and the other is via the moduli space of logarithmic stable maps. Our main result is a proof of the direct geometric relationship between these two spaces. For degree less than or equal to 3, we prove that the moduli space of logarithmic stable maps can be obtained by blowing up Vakil-Zinger’s desingularization.

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