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



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.

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

  • 1. Chen, X. Self rational maps of $ K3$ surfaces. Preprint, arXiv:1008.1619.
  • 2. Inose, H. Defining equations of singular $ K3$ surfaces and a notion of isogeny. Proceedings of the International Symposium on Algebraic Geometry, pp. 495-502, Kinokuniya Book Store, 1978. MR 578868 (81h:14021)
  • 3. Ma, S. On the 0-dimensional cusps of the Kähler moduli of a $ K3$ surface. Math. Ann. 348 (2010), no. 1, 57-80. MR 2657434 (2011g:14094)
  • 4. Mehran, A. Double cover of Kummer surfaces. Manuscripta Math. 123 (2007), 205-235. MR 2306633 (2008c:14052)
  • 5. Morrison, D. R. On $ K3$ surfaces with large Picard number. Invent. Math. 75 (1984), no. 1, 105-121. MR 728142 (85j:14071)
  • 6. Nikulin, V. V. Finite groups of automorphisms of Kahlerian $ K3$ surfaces. Trudy Moskov. Mat. Obshch. 38 (1979), 75-137. MR 544937 (81e:32033)
  • 7. Nikulin, V. V. On rational maps between $ K3$ surfaces. Constantin Carathéodory: An international tribute, 964-995, World Sci. Publ., 1991. MR 1130874 (92m:14049)
  • 8. Shioda, T. Kummer sandwich theorem of certain elliptic $ K3$ surfaces. Proc. Japan Acad. Ser. A. 82 (2006), no. 8, 137-140. MR 2279280 (2008b:14064)
  • 9. Shioda, T.; Inose, H. On singular $ K3$ surfaces. Complex analysis and algebraic geometry, pp. 119-136. Iwanami Shoten, 1977. MR 0441982 (56:371)

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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

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.