Moduli of PT-semistable objects II

Abstract

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable objects in $D^b(X)$ as an Artin stack of finite type that is universally closed. In the absence of strictly semistable objects, we construct the moduli as a proper algebraic space of finite type.

34 pages. Exposition improved based on referee's comments, especially the proofs of Prop 2.6 and 2.17 (of this version). References added; typos corrected. Openness and separatedness now in a separate section. Sections 4 and 5 of previous version removed. Accepted for publication by the Transactions of the American Mathematical Society. This is the sequel to http://arxiv.org/abs/1011.5688