稳定向量丛的模空间上的Hecke型有理曲线
Rational Curves of Hecke Type on Moduli Spaces of Stable Bundles
摘要: 设C是亏格为g≥2的光滑射影曲线，L为C上次数为d的线丛。令M:=SUC(r,L)是C上秩为r且具有固定行列式L的稳定向量丛的模空间，本文主要研究模空间M上的Hecke型有理曲线的次数与其定义向量丛在跳跃直线上的分裂情况和跳跃直线数量之间的关系，并给出一些Hecke型有理曲线的例子。
Abstract: Let C be a smooth projective curve of genus g≥2 and L be a line bundle on C of degree d. Let M:=SUC(r,L) be the moduli space of stable vector bundles on C of rank r and with the fixed determinant L. In this paper, we mainly study the relationship between the degree of a rational curve of Hecke type on moduli space M and the splitting of vector bundle E on jumping lines as well as that between the degree of a rational curve of Hecke type on moduli space M and the number of jumping lines, where the vector bundle E defines the rational curve of Hecke type. And we give some examples of rational curves of Hecke type.
文章引用：胡金成, 刘敏. 稳定向量丛的模空间上的Hecke型有理曲线[J]. 理论数学, 2022, 12(7): 1262-1268. https://doi.org/10.12677/PM.2022.127137

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