arXiv:math/0703590 Abstract

arXiv:math/0703590 [math.AG]Abstract References Reviews Resources

Moduli stacks and invariants of semistable objects on K3 surfaces

Published 2007-03-20, updated 2007-07-12Version 3

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.

Comments: 42pages

Categories: math.AG

Subjects: 14D20, 18E30

Keywords: moduli stack, k3 surface, stability condition, coherent sheaves, artin stack

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