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

Source 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 $r\geq2$ and degree $d$ on a smooth complex projective curve, assuming $g(C)\geq3$ and $\Aut(C)=1$. When the Jacobian $J(C)$ has endomorphism ring $\Z$, the partners are indexed by $(\Z/r\Z)^\times/\{\pm1\}$. 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.