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

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2017-08-12 DOI:10.14231/AG-2019-026

Luke Oeding, Claudiu Raicu, Steven V. Sam

引用次数: 5

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.

查看原文本刊更多论文

关于分段嵌入合子的(非)消失

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。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.