Minimal rational curves in moduli spaces of stable bundles

Details Minimal rational curves in moduli spaces of stable bundles Minimal rational curves in moduli spaces of stable bundles

2003-10-06

arxiv.org/abs/math/0310066v1

Mathematics

Algebraic Geometry

6 pages, amstex

Scientific paper

In this short note, we show that any rational curve passing through the
generic point in a moduli space of stable bundles with rank $r$ and fixed
determinant on a smooth projective curve of genus $g\ge 4$ has degree (with
respect to the anti-canonical line bundle of the moduli space) at least $2r$.
It has degree $2r$ if and only if it is a Hecke curve.

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