English

Hessian quartic surfaces that are Kummer surfaces

Algebraic Geometry 2007-05-23 v1

Abstract

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.

Keywords

Cite

@article{arxiv.math/9903037,
  title  = {Hessian quartic surfaces that are Kummer surfaces},
  author = {Joel E. Rosenberg},
  journal= {arXiv preprint arXiv:math/9903037},
  year   = {2007}
}

Comments

12 pages, LaTex/BibTeX