Derived equivalences of Azumaya algebras on K3 surfaces
Seminar Room 1, Newton Institute
We consider moduli spaces of Azumaya algebras on K3 surfaces. These correspond to twisted sheaves. We prove that when _(A) is zero and c2(A) is within 2r of its minimal bound, where r2 is the rank of A, then the moduli space if non empty is a smooth projective surface. We construct a moduli space of Azumaya algebras on the double cover of the projective plane. In some other special cases we prove a derived equivalence between K3 surfaces and moduli spaces of Azumaya algebras.