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The alternating group of degree 6 in the geometry of the Leech lattice and K3 surfaces

Published online by Cambridge University Press:  25 February 2005

JongHae Keum ,
Keiji Oguiso  and
De-Qi Zhang
JongHae Keum
Affiliation:
School of Mathematics, Korea Institute for Advanced Study, Dongdaemun-gu, Seoul 130-722, Korea. E-mail: jhkeum@kias.re.krSouth Korea
Keiji Oguiso
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba Meguro-ku, Tokyo 153-8914, Japan. E-mail: oguiso@ms.u-tokyo.ac.jp
De-Qi Zhang
Affiliation:
Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Singapore. E-mail: matzdq@math.nus.edu.sg
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Abstract

The alternating group of degree 6 is located at the junction of three series of simple non-commutative groups: simple sporadic groups, alternating groups and simple groups of Lie type. It plays a very special role in the theory of finite groups. We shall study its new roles both in a finite geometry of a certain pentagon in the Leech lattice and also in the complex algebraic geometry of K3 surfaces.

Keywords

alternating group of degree 6Leech latticeK3 surfaces14J2811H0620D0620D08
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 90 , Issue 2 , March 2005 , pp. 371 - 394
Copyright
2005 London Mathematical Society

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