Moduli stacks and invariants of semistable objects on K3 surfaces

Details Moduli stacks and invariants of semistable objects on K3 surfaces Moduli stacks and invariants of semistable objects on K3 surfaces

2007-03-20

arxiv.org/abs/math/0703590v3

Mathematics

Algebraic Geometry

42pages

Scientific paper

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.

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