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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Projectivity and birational geometry of Bridgeland moduli spaces
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by Arend Bayer and Emanuele Macrì PDF
J. Amer. Math. Soc. 27 (2014), 707-752 Request permission


We construct a family of nef divisor classes on every moduli space of stable complexes in the sense of Bridgeland. This divisor class varies naturally with the Bridgeland stability condition. For a generic stability condition on a K3 surface, we prove that this class is ample, thereby generalizing a result of Minamide, Yanagida, and Yoshioka. Our result also gives a systematic explanation of the relation between wall-crossing for Bridgeland-stability and the minimal model program for the moduli space.

We give three applications of our method for classical moduli spaces of sheaves on a K3 surface.

1. We obtain a region in the ample cone in the moduli space of Gieseker-stable sheaves only depending on the lattice of the K3.

2. We determine the nef cone of the Hilbert scheme of $n$ points on a K3 surface of Picard rank one when $n$ is large compared to the genus.

3. We verify the “Hassett-Tschinkel/Huybrechts/Sawon” conjecture on the existence of a birational Lagrangian fibration for the Hilbert scheme in a new family of cases.

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Additional Information
  • Arend Bayer
  • Affiliation: Department of Mathematics, University of Connecticut U-3009, 196 Auditorium Road, Storrs, Connecticut 06269-3009
  • Address at time of publication: School of Mathematics, The University of Edinburgh, James Clerk Maxwell Building, The King’s Buildings, Mayfield Road, Edinburgh, Scotland EH9 3JZ, United Kingdom
  • MR Author ID: 728427
  • Email:
  • Emanuele Macrì
  • Affiliation: Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210-1174
  • Email:
  • Received by editor(s): March 23, 2012
  • Received by editor(s) in revised form: April 8, 2013, and July 12, 2013
  • Published electronically: April 3, 2014
  • © Copyright 2014 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 27 (2014), 707-752
  • MSC (2010): Primary 14D20; Secondary 18E30, 14J28, 14E30
  • DOI:
  • MathSciNet review: 3194493