The strong maximal rank conjecture and moduli spaces of curves

IF 0.9 1区数学 Q2 MATHEMATICS

Algebra & Number Theory Pub Date : 2024-09-18 DOI:10.2140/ant.2024.18.1403

Fu Liu, Brian Osserman, Montserrat Teixidor i Bigas, Naizhen Zhang

引用次数: 0

Abstract

Building on recent work of the authors, we use degenerations to chains of elliptic curves to prove two cases of the Aprodu–Farkas strong maximal rank conjecture, in genus $22$ and $23$ . This constitutes a major step forward in Farkas’ program to prove that the moduli spaces of curves of genus $22$ and $23$ are of general type. Our techniques involve a combination of the Eisenbud–Harris theory of limit linear series, and the notion of linked linear series developed by Osserman.

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强最大秩猜想与曲线模空间

在作者近期工作的基础上，我们利用椭圆曲线链的退化证明了阿普罗杜-法卡斯强最大秩猜想的两种情况，即属22和23。这是法尔卡斯证明属 22 和 23 的曲线模空间为一般类型的计划的重要一步。我们的技术结合了艾森布-哈里斯极限线性级数理论和奥瑟曼提出的关联线性级数概念。

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

Algebra & Number Theory MATHEMATICS-

CiteScore

1.80

自引率

7.70%

发文量

审稿时长

6-12 weeks

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