导出范畴与空间曲线的亏格

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Emanuele Macrì, B. Schmidt
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引用次数: 16

摘要

我们将Grusson和Peskine关于射影空间中曲线亏格的一个经典结果推广到Picard秩为1的主极化阿贝尔三重。该证明基于导出类别中理想曲线槽的过墙技术。在此过程中,我们得到了其他稳定对象(如秩二滑轮)的Chern特征的界。该论点也给出了射影空间的一个证明。在这种情况下,这些技术也表明了Hartshorne和Hirschowitz的猜想的方法,我们证明了实现这一猜想的第一步。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Derived categories and the genus of space curves
We generalize a classical result about the genus of curves in projective space by Gruson and Peskine to principally polarized abelian threefolds of Picard rank one. The proof is based on wall-crossing techniques for ideal sheaves of curves in the derived category. In the process, we obtain bounds for Chern characters of other stable objects such as rank two sheaves. The argument gives a proof for projective space as well. In this case these techniques also indicate an approach for a conjecture by Hartshorne and Hirschowitz and we prove first steps towards it.
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来源期刊
Accounts of Chemical Research
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.
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