Proceedings of the American Mathematical Society

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On $ K3$ surfaces which dominate Kummer surfaces


Author: Shouhei Ma
Journal: Proc. Amer. Math. Soc. 141 (2013), 131-137
MSC (2010): Primary 14J28; Secondary 14E05
Published electronically: May 15, 2012
MathSciNet review: 2988717
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Abstract: We study isogeny relations between $ K3$ surfaces and Kummer surfaces. Specifically, we prove a Torelli-type theorem for the existence of rational maps from $ K3$ surfaces to Kummer surfaces, and a Kummer sandwich theorem for $ K3$ surfaces with Shioda-Inose structure.


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Additional Information

Shouhei Ma
Affiliation: Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan
Address at time of publication: Graduate School of Mathematics, Nagoya University, Furō-chō, Chikusa-ku, Nagoya 464-8602, Japan
Email: sma@ms.u-tokyo.ac.jp, ma@math.nagoya-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11302-4
Keywords: $K3$ surface, rational map, Shioda-Inose structure.
Received by editor(s): March 17, 2011
Received by editor(s) in revised form: June 12, 2011
Published electronically: May 15, 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.