Birational automorphisms of quartic Hessian surfaces

Details Birational automorphisms of quartic Hessian surfaces Birational automorphisms of quartic Hessian surfaces

2001-03-27

arxiv.org/abs/math/0103186v1

Mathematics

Algebraic Geometry

25 pages, 2 figures

Scientific paper

We find generators of the group of birational automorphisms of the Hessian surface of a general cubic surface. Its nonsingular minimal model is a K3 surface with the Picard lattice of rank 16. The latter embeds naturally in the even unimodular lattice $II^{1,25}$ of rank 26 and signature $(1,25)$ as the orthogonal complement of a root sublattice of rank 10. Our generators are related to reflections with respect to some Leech roots. A similar observation was made first in the case of quartic Kummer surfaces in the work of S. Kond$\bar {\roman o}$. We shall explain how our generators are related to the generators of the group of birational automorphisms of a general quartic Kummer surface which is birationally isomorphic to a special Hessian surface.

Affiliated with

Also associated with

No associations

Rating

Birational automorphisms of quartic Hessian surfaces does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Birational automorphisms of quartic Hessian surfaces, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Birational automorphisms of quartic Hessian surfaces will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-28470