Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

Bridgeland stability conditions on threefolds II: An application to Fujita's conjecture


Authors: Arend Bayer, Aaron Bertram, Emanuele Macrì and Yukinobu Toda
Journal: J. Algebraic Geom. 23 (2014), 693-710
DOI: https://doi.org/10.1090/S1056-3911-2014-00637-8
Published electronically: January 28, 2014
MathSciNet review: 3263665
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Abstract | References | Additional Information

Abstract: We apply a conjectured inequality on third Chern classes of stable two-term complexes on threefolds to Fujita's conjecture. More precisely, the inequality is shown to imply a Reider-type theorem in dimension three which in turn implies that $ K_X + 6L$ is very ample when $ L$ is ample, and that $ 5L$ is very ample when $ K_X$ is trivial.


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Additional Information

Arend Bayer
Affiliation: Department of Mathematics, University of Connecticut U-3009, 196 Auditorium Road, Storrs, Connecticut 06269-3009
Email: bayer@math.uconn.edu

Aaron Bertram
Affiliation: Department of Mathematics, University of Utah, 155 S 1400 E, Salt Lake City, Utah 84112
Email: bertram@math.utah.edu

Emanuele Macrì
Affiliation: Mathematical Institute, University of Bonn, Endenicher Allee 60, D-53115 Bonn, Germany; and 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/S1056-3911-2014-00637-8
Received by editor(s): June 23, 2011
Published electronically: January 28, 2014
Additional Notes: The first author was partially supported by NSF grant DMS-0801356/DMS-1001056
The second author was partially supported by NSF grant DMS-0901128
The third author was partially supported by NSF grant DMS-1001482/DMS-1160466, Hausdorff Center for Mathematics, Bonn, and by SFB/TR 45
The fourth 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 2014 University Press, Inc.

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