Journal of the Mathematical Society of Japan

K3 surfaces and sphere packings

Tetsuji SHIODA

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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

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

First available in Project Euclid: 5 November 2008

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Zentralblatt MATH identifier

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

K3 surface Mordell-Weil lattice Neron-Séveri lattice


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

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