Moduli spaces of sheaves on K3 surfaces and symplectic stacks

摘要

We view a moduli space of semistable sheaves on a K3 surface as a global quotient stack, and compute its cotangent complex in terms of the universal sheaf on the Quot scheme using the classical and reduced Atiyah classes. As an application, we define the notion of a symplectic stack, and show that it includes moduli stacks of semistable sheaves on K3 surfaces.