Communications in Analysis and Geometry
Volume 25 (2017)
Moduli spaces of sheaves on K3 surfaces and symplectic stacks
Pages: 1063 – 1106
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.
moduli space, K3 surface, cotangent complex, Atiyah class, GIT, symplectic structure
2010 Mathematics Subject Classification
Primary 14D20. Secondary 14J28, 18E30.
Paper received on 9 December 2015.