ncts

A Hecke curve is a rational curve on the moduli space $SU_C(r,d)$ of vector bundles over an algebraic curve, constructed by using the Hecke transformation. The Hecke curves played an important role in Jun-Muk Hwang's works on the geometry of $SU_C(r,d)$ . Later, Xiaotao Sun proved that they have the minimal degree among the rational curves passing through a general point. We construct rational curves on the moduli spaces of symplectic and orthogonal bundles by using symplectic/orthogonal versions of Hecke transformation. It turns out that the symplectic Hecke curves are special kind of Hecke curves, while the orthogonal Hecke curves have degree $2d$ , where $d$ is the degree of Hecke curves. Also we show that those curves have the minimal degree among the rational curves passing through a general point. This is a joint work with Kiryong Chung and Sanghyeon Lee.