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A note on Bogomolov-Gieseker type inequality for Calabi-Yau 3-folds


Author: Yukinobu Toda
Journal: Proc. Amer. Math. Soc. 142 (2014), 3387-3394
MSC (2010): Primary 14F05
DOI: https://doi.org/10.1090/S0002-9939-2014-12096-X
Published electronically: June 25, 2014
MathSciNet review: 3238415
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Abstract: The conjectural Bogomolov-Gieseker (BG) type inequality for tilt semistable objects on projective 3-folds was proposed by Bayer, Macri and the author. In this note, we prove our conjecture for slope stable sheaves with the smallest first Chern class on certain Calabi-Yau 3-folds, e.g. quintic 3-folds.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9939-2014-12096-X
Received by editor(s): January 29, 2012
Received by editor(s) in revised form: October 30, 2012
Published electronically: June 25, 2014
Additional Notes: This work was supported by a World Premier International Research Center Initiative (WPI initiative), MEXT, Japan. This work was also supported by Grant-in-Aid for Scientific Research grant (22684002), and partly (S-19104002), from the Ministry of Education, Culture, Sports, Science and Technology, Japan
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.