Elliptic curves in moduli space of stable bundles

Details Elliptic curves in moduli space of stable bundles Elliptic curves in moduli space of stable bundles

2010-11-19

arxiv.org/abs/1011.4482v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

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 $g\ge 2$. 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.

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