Elliptic Curves in Moduli Space of Stable Bundles

Let M be the moduli space of rank 2 stable bundles with fixed determinant of degree 1 on a smooth projective curve C of genus g >= 2. When C is generic, we show that any elliptic curve on M has degree (respect to anti-canonical divisor -K-M) at least 6, and we give a complete classification for elliptic curves of degree 6. Moreover, if g > 4, we show that any elliptic curve passing through the generic point of M has degree at least 12. We also formulate a conjecture for higher rank.