Moduli of PT-semistable objects II

2010/11/29 by Lo, Jason
#14D20 #14F05 #14J30 #14J60 #18E30 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1011.6306

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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