通用博维尔猜想

IF 1.2 2区数学 Q1 MATHEMATICS

Forum of Mathematics Sigma Pub Date : 2024-04-08 DOI:10.1017/fms.2024.21

Izzet Coskun, Eric Larson, Isabel Vogt

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引用次数: 0

摘要

让 $alpha \colon X \to Y$ 是光滑曲线的有限盖。博维尔猜想，如果 Y 的属至少为 1$，则一般向量束在 $\alpha $ 下的前推是半稳定的；如果 Y 的属至少为 2$，则前推是稳定的。如果 $\alpha $ 映射在任意光滑曲线 Y 的盖的赫维茨空间的任意分量中是一般的，我们就证明了这个猜想。

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Generic Beauville’s Conjecture

Let

$\alpha \colon X \to Y$

be a finite cover of smooth curves. Beauville conjectured that the pushforward of a general vector bundle under

$\alpha $

is semistable if the genus of Y is at least

$1$

and stable if the genus of Y is at least

$2$

. We prove this conjecture if the map

$\alpha $

is general in any component of the Hurwitz space of covers of an arbitrary smooth curve Y.

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来源期刊

Forum of Mathematics Sigma Mathematics-Statistics and Probability

CiteScore

1.90

自引率

5.90%

发文量

审稿时长

40 weeks

期刊介绍： Forum of Mathematics, Sigma is the open access alternative to the leading specialist mathematics journals. Editorial decisions are made by dedicated clusters of editors concentrated in the following areas: foundations of mathematics, discrete mathematics, algebra, number theory, algebraic and complex geometry, differential geometry and geometric analysis, topology, analysis, probability, differential equations, computational mathematics, applied analysis, mathematical physics, and theoretical computer science. This classification exists to aid the peer review process. Contributions which do not neatly fit within these categories are still welcome. Forum of Mathematics, Pi and Forum of Mathematics, Sigma are an exciting new development in journal publishing. Together they offer fully open access publication combined with peer-review standards set by an international editorial board of the highest calibre, and all backed by Cambridge University Press and our commitment to quality. Strong research papers from all parts of pure mathematics and related areas will be welcomed. All published papers will be free online to readers in perpetuity.