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Heisenberg-invariant kummer surfaces

Published online by Cambridge University Press:  20 January 2009

K. Hulek ,
I. Nieto  and
G. K. Sankaran
K. Hulek
Affiliation:
Institut für Mathematik, Universität Hannover, Postfach 6009, D 30060 Hannover, Germany ([email protected])
I. Nieto
Affiliation:
Cimat, A.C., Callejon de Jalisco S/N, Col. Mineral de Valenciana, 36000 Guanajuato, Gto., Mexico ([email protected])
G. K. Sankaran
Affiliation:
Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK ([email protected])
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Abstract

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We study, from the point of view of abelian and Kummer surfaces and their moduli, the special quintic threefold known as Nieto's quintic. It is, in some ways, analogous to the Segre cubic and the Burkhardt quartic and can be interpreted as a moduli space of certain Kummer surfaces. It contains 30 planes and has 10 singular points: we describe how some of these arise from bielliptic and product abelian surfaces and their Kummer surfaces.

Keywords

abelian surfaceKummer surfacemoduliclassical algebraic geometry
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 43 , Issue 2 , June 2000 , pp. 425 - 439
Copyright
Copyright © Edinburgh Mathematical Society 2000

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