Equivariant categories of symplectic surfaces and fixed loci of Bridgeland moduli spaces - Beckmann, Thorsten; Oberdieck, Georg (Algebraic geometry, 2022)
Given an action of a ﬁnite group G on the derived category of a smooth projective variety X, we relate the ﬁxed loci of the induced G-action on moduli spaces of stable objects in Db(Coh(X)) with moduli spaces of stable objects in the equivariant category Db(Coh(X))G. As an application, we obtain a criterion for the equivariant category of a symplectic action on the derived category of a symplectic surface to be equivalent to the derived category of a surface. This generalizes the derived McKay correspondence and yields a general framework for describing ﬁxed loci of symplectic group actions on moduli spaces of stable objects on symplectic surfaces.
Gesehen am 12.12.2024