论文标题
曲线上均匀程度的对称能力的对称能力的稳定性
Stability of symmetric powers of vector bundles of rank two with even degree on a curve
论文作者
论文摘要
本文将稳定的矢量捆绑包$ e $等级的对称力的严格半稳定性在平滑的投影曲线$ c $ c $ c $ g \ geq 2 $上均为$ 2 $。 $ s^2 e $的严格半稳定性等于$ e $的正交性或在自我交流号为零的规则表面$ \ mathbb {p} _C（e）$上存在分分线的存在。本文通过基本变换研究了两种解释之间的关系。本文还提供了$ e $的分类，并具有严格的半稳定$ s^3 e $。此外，可以表明，当$ s^2 e $稳定时，每个对称的功率$ s^k e $均稳定，除了稳定的vector vector套件中有限数量的$ e $等级$ 2 $的$ e $，均为$ c $的固定确定性。
This paper treats the strict semi-stability of the symmetric powers $S^k E$ of a stable vector bundle $E$ of rank $2$ with even degree on a smooth projective curve $C$ of genus $g \geq 2$. The strict semi-stability of $S^2 E$ is equivalent to the orthogonality of $E$ or the existence of a bisection on the ruled surface $\mathbb{P}_C(E)$ whose self-intersection number is zero. A relation between the two interpretations is investigated in this paper through elementary transformations. This paper also gives a classification of $E$ with strictly semi-stable $S^3 E$. Moreover, it is shown that when $S^2 E$ is stable, every symmetric power $S^k E$ is stable for all but a finite number of $E$ in the moduli of stable vector bundles of rank $2$ with fixed determinant of even degree on $C$.
