Moduli stacks and invariants of semistable objects on K3 surfaces

Abstract

For a K3 surface X and its bounded derived category of coherent sheaves D(X), we have the notion of stability conditions on D(X) in the sense of T.Bridgeland. In this paper, we show that the moduli stack of semistable objects in D(X) with a fixed numerical class and a phase is represented by an Artin stack of finite type over C. Then following D.Joyce's work, we introduce the invariants counting semistable objects in D(X), and show that the invariants are independent of a choice of a stability condition.

42pages

References in corpus (7)

• Dirichlet branes, homological mirror symmetry, and stability
• Stability conditions on a non-compact Calabi-Yau threefold
• Spaces of stability conditions
• Holomorphic generating functions for invariants counting coherent sheaves on Calabi-Yau 3-folds
• Some examples of spaces of stability conditions on derived categories
• Stability Conditions and Branes at Singularities
• Motivic invariants of Artin stacks and 'stack functions'

Cited by in corpus (2)

• Crossing the Wall: Branes vs. Bundles
• Bridgeland's stabilities on abelian surfaces