论文标题
关于等级2线性系列的线性稳定性和共济稳定性
On linear stability and syzygy stability for rank 2 linear series
论文作者
论文摘要
在以前的作品中，作者研究了曲线$ c $上生成的线性系列$ | V | $的线性稳定性与矢量束$ m_ {v，l}的斜率稳定性之间的关系：= \ ker（v \ otimes \ otcal \ nathcal \ Mathcal {O} {O} _c \ t）$。特别是，第二个名称的作者和L. potpino的猜想是，对于完整的线性系统$ | l | $，线性（半）稳定性相当于$ m_v $的斜率（半）稳定性，而第一个和第三名的作者证明，这种猜想的性超ellirtiriptic和通用曲线适用。 在这项工作中，我们在任何平滑的平面曲线$ 7 $上为此猜想提供了反例。
In previous works, the authors investigated the relationships between linear stability of a generated linear series $|V|$ on a curve $C$, and slope stabillity of the vector bundle $M_{V,L} := \ker (V \otimes \mathcal{O}_C \to L)$. 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 $M_V$, and the first and third named authors proved that this conjecture holds for hyperelliptic and for generic curves. In this work we provide a counterexample to this conjecture on any smooth plane curve of degree $7$.
