Moduli of PT-Semistable Objects I

Details Moduli of PT-Semistable Objects I Moduli of PT-Semistable Objects I

2010-11-25

arxiv.org/abs/1011.5688v1

J. Algebra, Vol. 339 (1), pp. 203-222, 2011

Mathematics

Algebraic Geometry

23 pages

Scientific paper

10.1016/j.jalgebra.2011.04.035

We show boundedness for PT-semistable objects of any Chern classes on a smooth projective three-fold $X$. Then we show that the stack of objects in the heart $\langle \Coh_{\leq 1}(X), \Coh_{\geq 2}(X)[1] \rangle$ satisfies a version of the valuative criterion for completeness. In the remainder of the paper, we give a series of results on how to compute cohomology with respect to this heart.

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