Open Access
May 2000 A note on $K3$ surfaces and sphere packings
Tetsuji Shioda
Proc. Japan Acad. Ser. A Math. Sci. 76(5): 68-72 (May 2000). DOI: 10.3792/pjaa.76.68


We study the Mordell-Weil lattices ([9]) of the elliptic $K3$ surfaces which have been introduced by Inose [4] and Kuwata [6]. The point is that the lattices (of rank up to 18) arising this way can be of some interest in terms of sphere packings. In this note, we treat the case of rank 16, 17, or 18, and show that these Morderll-Weil lattices are potentially comparable with the record lattices in these dimensions ([2]). The detailed accont is in preparation, which will include the corresponding results for other dimensions as well.


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Tetsuji Shioda. "A note on $K3$ surfaces and sphere packings." Proc. Japan Acad. Ser. A Math. Sci. 76 (5) 68 - 72, May 2000.


Published: May 2000
First available in Project Euclid: 23 May 2006

zbMATH: 0982.14024
MathSciNet: MR1771143
Digital Object Identifier: 10.3792/pjaa.76.68

Primary: 11H31 , 14J27 , 14J28

Keywords: $K3$ surface , Mordell-Weil lattice , sphere packings

Rights: Copyright © 2000 The Japan Academy

Vol.76 • No. 5 • May 2000
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