论文标题
在符号和正交束的模量空间上的最小有理曲线
Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles
论文作者
论文摘要
令$ c $是$ g $属的代数曲线，而每行$ $ $ $ c $ co $。令$ \ MATHCAL {MS} _C（N，L）$和$ \ MATHCAL {MO} _C（N，L）$分别为$ L $ VALAUDE symplectic和正交捆绑包的Moduli空间，超过$ C $ n $ n $ n $。我们在这些模量空间上构建有理曲线，这些曲线将Hecke曲线推广到向量束的模量空间上。作为主要结果，我们表明这些Hecke型曲线在穿过模量空间的一般点的有理曲线之间具有最小的程度。作为其副产品，我们显示了非亚洲托雷利定理并计算模量空间的自动形态。
Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$. Let $\mathcal{MS}_C(n,L)$ and $\mathcal{MO}_C(n,L)$ be the moduli spaces of $L$-valued symplectic and orthogonal bundles respectively, over $C$ of rank $n$. We construct rational curves on these moduli spaces which generalize Hecke curves on the moduli space of vector bundles. As a main result, we show that these Hecke type curves have the minimal degree among the rational curves passing through a general point of the moduli spaces. As its byproducts, we show the non-abelian Torelli theorem and compute the automorphism group of moduli spaces.
