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classical algebraic geometry

Proceedings of the Edinburgh Mathematical Society (1)

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Heisenberg-invariant kummer surfaces
K. Hulek, I. Nieto, G. K. Sankaran
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 2 / June 2000

Published online by Cambridge University Press:

20 January 2009, pp. 425-439
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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.