Journal of the Mathematical Society of Japan

K3 surfaces and sphere packings

Tetsuji SHIODA

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Abstract

We determine the structure of the Mordell-Weil lattice, Néron-Severi lattice and the lattice of transcendental cycles for certain elliptic K3 surfaces. We find that such questions from algebraic geometry are closely related to the sphere packing problem, and a key ingredient is the use of the sphere packing bounds in establishing geometric results.

Article information

Source
J. Math. Soc. Japan, Volume 60, Number 4 (2008), 1083-1105.

Dates
First available in Project Euclid: 5 November 2008

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1225894034

Digital Object Identifier
doi:10.2969/jmsj/06041083

Mathematical Reviews number (MathSciNet)
MR2467871

Zentralblatt MATH identifier
1178.14038

Subjects
Primary: 14J27: Elliptic surfaces 14J28: $K3$ surfaces and Enriques surfaces 14H40: Jacobians, Prym varieties [See also 32G20]

Keywords
K3 surface Mordell-Weil lattice Neron-Séveri lattice

Citation

SHIODA, Tetsuji. K3 surfaces and sphere packings. J. Math. Soc. Japan 60 (2008), no. 4, 1083--1105. doi:10.2969/jmsj/06041083. https://projecteuclid.org/euclid.jmsj/1225894034


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References

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