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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Moduli of PT-semistable objects II


Author: Jason Lo
Journal: Trans. Amer. Math. Soc. 365 (2013), 4539-4573
MSC (2010): Primary 14F05, 14D20, 18E30, 14J60; Secondary 14J30
Published electronically: March 5, 2013
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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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Additional Information

Jason Lo
Affiliation: Department of Mathematics, Building 380, Stanford University, Stanford, California 94305
Address at time of publication: Department of Mathematics, 202 Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65211
Email: locc@missouri.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05622-X
PII: S 0002-9947(2013)05622-X
Keywords: PT-stability, semistable reduction, derived category, moduli, valuative criterion
Received by editor(s): November 30, 2010
Received by editor(s) in revised form: May 3, 2011
Published electronically: March 5, 2013
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.