K3 Polytopes and their Quartic Surfaces
Algebraic Geometry
2019-07-17 v2 Combinatorics
Abstract
K3 polytopes appear in complements of tropical quartic surfaces. They are dual to regular unimodular central triangulations of reflexive polytopes in the fourth dilation of the standard tetrahedron. Exploring these combinatorial objects, we classify K3 polytopes with up to vertices. Their number is . We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.
Cite
@article{arxiv.1806.02236,
title = {K3 Polytopes and their Quartic Surfaces},
author = {Gabriele Balletti and Marta Panizzut and Bernd Sturmfels},
journal= {arXiv preprint arXiv:1806.02236},
year = {2019}
}