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

초록

Let C$C$ be an algebraic curve of genus g$g$ and L$L$ a line bundle over C$C$. Let MSC(n,L)$\mathcal{M}{S}_C(n,L)$ and MOC(n,L)$\mathcal{M}{O}_C(n,L)$ be the moduli spaces of L$L$-valued symplectic and orthogonal bundles, respectively, over C$C$ of rank n$n$. We construct rational curves of Hecke type on these moduli spaces which generalize the Hecke curves on the moduli space of vector bundles. As a main result, we show that these curves have the minimal degree among the rational curves passing through a general point of the moduli spaces. As its by-products, we show the non-abelian Torelli theorem and compute the automorphism group of the moduli spaces.

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