Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


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
MathSciNet review: 3091762
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

  • 1. W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergeb. Math. Grenzgebiete 4, Springer, Berlin, 1984. MR 749574 (86c:32026)
  • 2. S. Boissière, Automorphismes naturels de l'espace de Douady de points sur une surface, Canad. J. Math. 64 (2012), 3-23. MR 2932167
  • 3. S. Boissière and A. Sarti, A note on automorphisms and birational transformations of holomorphic symplectic manifolds, Proceedings of Amer. Math. Soc. 140 (2012), no. 12, 4053-4062. MR 2957195
  • 4. S. Boissière, M. Nieper-Wisskirchen, and A. Sarti, Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties, Journal de Mathématiques Pures et Appliquées 95 (5) (2011), 553-563. MR 2786223
  • 5. M. Gross, D. Huybrechts, and D. Joyce, Calabi-Yau manifolds and related geometries, Springer, Berlin, 2003. MR 1963559 (2004c:14075)
  • 6. V. Nikulin, Finite automorphism groups of Kähler $ K3$ surfaces, Trans. Mosc. Math. Soc. 2 (1980), 71-135. MR 0544937 (81e:32033)
  • 7. K. Oguiso, Tits alternative in hyperkähler manifolds, Mah. Res. Lett. 13 (2006), 307-316. MR 2231119 (2007e:14023)
  • 8. K. Oguiso and S. Schröer, Enriques manifolds, J. Reine Angew. Math. 661 (2011), 215-235. MR 2863907

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14E05, 14J28, 14J32, 14J40

Retrieve articles in all journals with MSC (2010): 14E05, 14J28, 14J32, 14J40

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

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

American Mathematical Society