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 Poincare 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 \(g \ge 2\).