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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Raynaud-Mukai construction and Calabi-Yau threefolds in positive characteristic


Author: Yukihide Takayama
Journal: Proc. Amer. Math. Soc. 140 (2012), 4063-4074
MSC (2010): Primary 14F17, 14J32; Secondary 14M99, 14J45
Published electronically: April 5, 2012
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Abstract: In this article, we study the possibility of producing a Calabi-Yau threefold in positive characteristic which is a counterexample to Kodaira vanishing. The only known method to construct the counterexample is the so-called inductive method such as the Raynaud-Mukai construction or Russel construction. We consider Mukai's method and its modification. Finally, as an application of the Shepherd-Barron vanishing theorem of Fano threefolds, we compute $ H^1(X, H^{-1})$ for any ample line bundle $ H$ on a Calabi-Yau threefold $ X$ on which Kodaira vanishing fails.


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Yukihide Takayama
Affiliation: Department of Mathematical Sciences, Ritsumeikan University, 1-1-1 Nojihigashi, Kusatsu, Shiga 525-8577, Japan
Email: takayama@se.ritsumei.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11271-7
PII: S 0002-9939(2012)11271-7
Received by editor(s): October 18, 2010
Received by editor(s) in revised form: May 2, 2011, and May 21, 2011
Published electronically: April 5, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.