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Minimal rational curves in moduli spaces of stable bundles

Xiaotao Sun
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Abstract

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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Xiaotao Sun. 2003-10-06. Minimal rational curves in moduli spaces of stable bundles. https://arxiv.org/abs/math/0310066

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