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Every algebraic Kummer surface is the K3-cover of an Enriques surface

Published online by Cambridge University Press:  22 January 2016

Jong Hae Keum
Jong Hae Keum*
Affiliation:
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA
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A Kummer surface is the minimal desingularization of the surface T/i, where T is a complex torus of dimension 2 and i the involution automorphism on T. T is an abelian surface if and only if its associated Kummer surface is algebraic. Kummer surfaces are among classical examples of K3-surfaces (which are simply-connected smooth surfaces with a nowhere-vanishing holomorphic 2-form), and play a crucial role in the theory of K3-surfaces. In a sense, all Kummer surfaces (resp. algebraic Kummer surfaces) form a 4 (resp. 3)-dimensional subset in the 20 (resp. 19)-dimensional family of K3-surfaces (resp. algebraic K3 surfaces).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 118 , June 1990 , pp. 99 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1990

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