Moduli of PT-semistable objects II

Lo, Jason

doi:10.1090/S0002-9947-2013-05622-X

Moduli of PT-semistable objects II
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Trans. Amer. Math. Soc. 365 (2013), 4539-4573 Request permission

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.

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