Basepoint-freeness thresholds and higher syzygies of abelian threefolds

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2020-08-24 DOI:10.14231/ag-2022-023

Atsushi Ito

引用次数: 9

Abstract

For a polarized abelian variety, Z. Jiang and G. Pareschi introduce an invariant and show that the polarization is basepoint free or projectively normal if the invariant is small. Their result is generalized to higher syzygies by F. Caucci, that is, the polarization satisfies property $(N_p)$ if the invariant is small. In this paper, we study a relation between the invariant and degrees of abelian subvarieties with respect to the polarization. For abelian threefolds, we give an upper bound of the invariant using degrees of abelian subvarieties. In particular, we affirmatively answer a question about $(N_p)$ on abelian varieties asked by the author and V. Lozovanu in the three dimensional case.

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基点自由阈值和阿贝尔三倍的高协同性

对于极化阿贝尔变种，Z.Jiang和G.Pareschi引入了一个不变量，并证明了如果不变量很小，极化是无基点的或投影正规的。他们的结果被F.Caucci推广到更高的系统，即如果不变量小，则极化满足性质$（N_p）$。在本文中，我们研究了阿贝尔子变种的不变量和度与极化之间的关系。对于阿贝尔三重，我们利用阿贝尔子变种的度给出了不变量的上界。特别地，我们肯定地回答了作者和V.Lozovanu在三维情况下提出的关于阿贝尔变种上的$（N_p）$的问题。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.