Derived Categories of Moduli Spaces of Vector Bundles on Curves II

Abstract

Let X be a smooth projective curve of genus g over $\mathbb {C}$ and M be the moduli space of stable vector bundle of rank 2 and determinant isomorphic to a fixed line bundle of degree 1 on X. Let E be the Poincaré bundle on $X \times M$ and $\Phi _E : D^b(X) \rightarrow D^b(M)$ Fourier–Mukai functor defined by E. It was proved in our earlier paper that $\Phi _E$ is fully faithful for every smooth projective curve of genus $g \ge 4.$ It is proved in this present paper that the result is also true for non-hyperelliptic curves of genus 3. Combining known results in the case of hyperelliptic curves, one obtains that $\Phi _E$ is fully faithful for all X of genus $g \ge 2$.

To Kumar Murty on his sixtieth birthday