Hessian quartic surfaces that are Kummer surfaces

Details Hessian quartic surfaces that are Kummer surfaces Hessian quartic surfaces that are Kummer surfaces

1999-03-07

arxiv.org/abs/math/9903037v1

Mathematics

Algebraic Geometry

12 pages, LaTex/BibTeX

Scientific paper

In 1899, Hutchinson presented a way to obtain a three-parameter family of Hessians of cubic surfaces as blowups of Kummer surfaces. We show that this family consists of those Hessians containing an extra class of conic curves. Based on this, we find the invariant of a cubic surface C in pentahedral form that vanishes if its Hessian is in Hutchinson's family, and we give an explicit map between cubic surfaces in pentahedral form and blowups of Kummer surfaces.

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