Fourier-Mukai partners and autoequivalences of moduli spaces of vector bundles

Abstract

We classify the smooth projective Fourier--Mukai partners and determine the derived autoequivalence group of the moduli space $U_C(r,d)$ of stable bundles of coprime rank $r\ge 2$ and degree $d$ on a smooth complex projective curve, assuming $g(C)\ge 3$ and $\Aut(C)=1$. When the Jacobian $J(C)$ has endomorphism ring $\mathbb{Z}$, the partners are indexed by $(\mathbb{Z}/r\mathbb{Z}{)}^{\times }/\{\pm 1\}$. We also prove that two coprime moduli spaces of vector bundles over complex curves of genus at least four are derived equivalent if and only if they are isomorphic.

arXiv comment26 pages