Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Bridgeland stability conditions on threefolds I: Bogomolov-Gieseker type inequalities


Authors: Arend Bayer, Emanuele Macrì and Yukinobu Toda
Journal: J. Algebraic Geom. 23 (2014), 117-163
DOI: https://doi.org/10.1090/S1056-3911-2013-00617-7
Published electronically: July 29, 2013
MathSciNet review: 3121850
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Abstract | References | Additional Information

Abstract: We construct new t-structures on the derived category of coherent
sheaves on smooth projective threefolds. We conjecture that they give Bridgeland stability conditions near the large volume limit. We show that this conjecture is equivalent to a Bogomolov-Gieseker type inequality for the third Chern character of certain stable complexes. We also conjecture a stronger inequality, and prove it in the case of projective space, and for various examples.

Finally, we prove a version of the classical Bogomolov-Gieseker inequality, not involving the third Chern character, for stable complexes.


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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
Email: bayer@math.uconn.edu

Emanuele Macrì
Affiliation: Mathematical Institute, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany & Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, Utah 84112
Address at time of publication: Department of Mathematics, The Ohio State University, 231 W 18th Avenue, Columbus, Ohio 43210
Email: macri.6@math.osu.edu

Yukinobu Toda
Affiliation: Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Japan
Email: yukinobu.toda@ipmu.jp

DOI: https://doi.org/10.1090/S1056-3911-2013-00617-7
Received by editor(s): January 23, 2011
Received by editor(s) in revised form: January 25, 2012
Published electronically: July 29, 2013
Additional Notes: The first author was partially supported by NSF grants DMS-0801356/DMS-1001056 and DMS-1101377. The second author was partially supported by NSF grant DMS-1001482/DMS-1160466, and by the Hausdorff Center for Mathematics, Bonn, and SFB/TR 45. The third author was supported by World Premier International Research Center Initiative (WPI initiative), MEXT, Japan, and Grant-in Aid for Scientific Research grant (22684002), partly (S-19104002), from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
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