Minimal rational curves on the moduli spaces of symplectic and orthogonal bundles

Abstract

Let $C$ be an algebraic curve of genus $g$ and $L$ a line bundle over $C$. Let ${\mathcal{MS}}_C(n,L)$ and ${\mathcal{M}\mathcal{O}}_C(n,L)$ 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.

23 pages

References in corpus (1)

• Moduli spaces of orthogonal bundles over an algebraic curve