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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Sections of Calabi-Yau threefolds with K3 fibration


Author: Zhiyuan Li
Journal: Trans. Amer. Math. Soc. 366 (2014), 6313-6328
MSC (2010): Primary 14-XX
Published electronically: June 10, 2014
MathSciNet review: 3267011
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Abstract: We study sections of a Calabi-Yau threefold fibered over a curve by K3 surfaces. We show that there exist infinitely many isolated sections on certain K3 fibered Calabi-Yau threefolds and that the group of algebraic $ 1$-cycles generated by these sections modulo algebraic equivalence is not finitely generated. We also give examples of K$ 3$ surfaces over the function field $ F$ of a complex curve with Zariski dense $ F$-rational points, whose geometric model is Calabi-Yau.


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Additional Information

Zhiyuan Li
Affiliation: Department of Mathematics, Building 380, Stanford University, 450 Serra Mall, Stanford, California 94305
Email: zli2@stanford.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2014-06002-9
Received by editor(s): June 6, 2012
Received by editor(s) in revised form: October 29, 2012
Published electronically: June 10, 2014
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.