Equivariant autoequivalences for finite group actions

Research paper by David Ploog

Indexed on: 30 Aug '05Published on: 30 Aug '05Published in: Mathematics - Algebraic Geometry


The familiar Fourier-Mukai technique can be extended to an equivariant setting where a finite group $G$ acts on a smooth projective variety $X$. In this paper we compare the group of invariant autoequivalences $\Aut(D(X))^G$ with the group of autoequivalences of $D^G(X)$. We apply this method in three cases: Hilbert schemes on K3 surfaces, Kummer surfaces and canonical quotients.