Moduli of PT-semistable objects II

Details Moduli of PT-semistable objects II Moduli of PT-semistable objects II

2010-11-29

arxiv.org/abs/1011.6306v2

Mathematics

Algebraic Geometry

34 pages. Exposition improved based on referee's comments, especially the proofs of Prop 2.6 and 2.17 (of this version). Refer

Scientific paper

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.

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