Communications in Analysis and Geometry

Volume 25 (2017)

Number 5

Moduli spaces of sheaves on K3 surfaces and symplectic stacks

Pages: 1063 – 1106



Ziyu Zhang (Mathematical Institute, University of Bonn, Germany; and Institute for Algebraic Geometry, Leibniz University, Hannover, Germany)


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.

Received 9 December 2015

Published 30 November 2017