Symmetric products and moduli spaces of vector bundles of curves

Let X be a smooth projective curve of genus g ≥ 2 and M be the moduli space of rank 2 stable vector bundles on X whose determinants are isomorphic to a fixed odd degree line bundle L. There has been a lot of works studying the moduli and recently the bounded derived category of coherent sheaves on M draws lots of attentions. It was proved that the derived category of X can be embedded into the derived category of M (cf. [11, 27, 28]). In this paper we prove that the derived category of the second symmetric product of X can be embedded into derived category of M when X is non-hyperelliptic and g ≥ 16.

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