关于分段嵌入合子的(非)消失

IF 1.2 1区数学 Q1 MATHEMATICS

Algebraic Geometry Pub Date : 2017-08-12 DOI:10.14231/AG-2019-026

Luke Oeding, Claudiu Raicu, Steven V. Sam

{"title":"关于分段嵌入合子的(非)消失","authors":"Luke Oeding, Claudiu Raicu, Steven V. Sam","doi":"10.14231/AG-2019-026","DOIUrl":null,"url":null,"abstract":"We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our bounds are tight for Segre embeddings of products of P^1. This generalizes results of Rubei concerning the Green-Lazarsfeld property N_p for Segre embeddings. Our methods combine the Kempf-Weyman geometric technique for computing syzygies, the Ein-Erman-Lazarsfeld approach to proving non-vanishing of Betti numbers, and the theory of algebras with straightening laws.","PeriodicalId":48564,"journal":{"name":"Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2017-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"On the (non-)vanishing of syzygies of Segre embeddings\",\"authors\":\"Luke Oeding, Claudiu Raicu, Steven V. Sam\",\"doi\":\"10.14231/AG-2019-026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our bounds are tight for Segre embeddings of products of P^1. This generalizes results of Rubei concerning the Green-Lazarsfeld property N_p for Segre embeddings. Our methods combine the Kempf-Weyman geometric technique for computing syzygies, the Ein-Erman-Lazarsfeld approach to proving non-vanishing of Betti numbers, and the theory of algebras with straightening laws.\",\"PeriodicalId\":48564,\"journal\":{\"name\":\"Algebraic Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2017-08-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.14231/AG-2019-026\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.14231/AG-2019-026","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 5

摘要

我们分析了投影空间乘积的Segre嵌入的分次Betti数的消失和不消失行为。当Betti表的每一行变为非零时，我们给出了下界，并证明了我们的界对于P^1的乘积的Segre嵌入是紧的。这推广了Rubei关于Segre嵌入的Green Lazarsfeld性质N_ p的结果。我们的方法结合了用于计算系统的Kempf-Weyman几何技术、用于证明Betti数不消失的Ein-Erman-Lazarsfeld方法以及具有矫直律的代数理论。

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

On the (non-)vanishing of syzygies of Segre embeddings

We analyze the vanishing and non-vanishing behavior of the graded Betti numbers for Segre embeddings of products of projective spaces. We give lower bounds for when each of the rows of the Betti table becomes non-zero, and prove that our bounds are tight for Segre embeddings of products of P^1. This generalizes results of Rubei concerning the Green-Lazarsfeld property N_p for Segre embeddings. Our methods combine the Kempf-Weyman geometric technique for computing syzygies, the Ein-Erman-Lazarsfeld approach to proving non-vanishing of Betti numbers, and the theory of algebras with straightening laws.

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

Algebraic Geometry Mathematics-Geometry and Topology

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

52 weeks

期刊介绍： This journal is an open access journal owned by the Foundation Compositio Mathematica. The purpose of the journal is to publish first-class research papers in algebraic geometry and related fields. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.