关于线性稳定性和系统稳定性

IF 0.4 4区数学 Q4 MATHEMATICS

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg Pub Date : 2022-05-30 DOI:10.1007/s12188-022-00258-2

Abel Castorena, Ernesto C. Mistretta, Hugo Torres-López

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引用次数: 0

摘要

在以前的工作中，作者研究了曲线C上生成的线性级数|V|的线性稳定性与syzygy向量丛\（M_{V，L}：=\ker（V\otimes\mathcal{O}_C\rightarrow L）\）。特别是，第二位作者和L.Stoppino猜想，对于一个完整的线性系统|L|，线性（半）稳定性等价于\（M_{L}\）的斜率（半）稳定。第一和第三位作者证明了这一猜想在两种相反的情况下成立：超椭圆曲线和一般曲线。在这项工作中，我们为这个猜想提供了一个反例，在任何7度的光滑平面曲线上。

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On linear stability and syzygy stability

In previous works, the authors investigated the relationships between linear stability of a generated linear series |V| on a curve C, and slope stability of the syzygy vector bundle \(M_{V,L} := \ker (V \otimes \mathcal {O}_C \rightarrow L)\). In particular, the second named author and L. Stoppino conjecture that, for a complete linear system |L|, linear (semi)stability is equivalent to slope (semi)stability of \(M_{L}\). The first and third named authors proved that this conjecture holds in the two opposite cases: hyperelliptic and generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree 7.

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来源期刊

Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 数学-数学

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The first issue of the "Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg" was published in the year 1921. This international mathematical journal has since then provided a forum for significant research contributions. The journal covers all central areas of pure mathematics, such as algebra, complex analysis and geometry, differential geometry and global analysis, graph theory and discrete mathematics, Lie theory, number theory, and algebraic topology.