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

 

Higher dimensional Enriques varieties with even index


Author: Jin Hong Kim
Journal: Proc. Amer. Math. Soc. 141 (2013), 3701-3707
MSC (2010): Primary 14E05, 14J28, 14J32, 14J40
Published electronically: July 12, 2013
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Abstract: Let $ Y$ be an Enriques variety of complex dimension $ 2n-2$ with $ n\ge 2$. Assume that $ n=2m$ for odd prime $ m$. In this paper we show that $ Y$ is the quotient of a product of a Calabi-Yau manifold of dimension $ 2m$ and an irreducible holomorphic symplectic manifold of dimension $ 2m-2$ by an automorphism of order $ n$ acting freely. We also show that both $ Y$ and its universal cover are always projective.


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Additional Information

Jin Hong Kim
Affiliation: Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology, Yuseong-gu, Daejeon 305–701, Republic of Korea
Address at time of publication: Department of Mathematics Education, Chosun University, 309 Pilmun-daero, Dong-gu, Gwangju 501-759, Republic of Korea
Email: jinhkim11@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11650-3
PII: S 0002-9939(2013)11650-3
Keywords: Enriques varieties, Calabi-Yau manifolds, holomorphic symplectic manifolds, index
Received by editor(s): September 20, 2011
Received by editor(s) in revised form: January 6, 2012, and January 11, 2012
Published electronically: July 12, 2013
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society