Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
MiS Preprint
40/2018
K3 Polytopes and their Quartic Surfaces
Gabriele Baletti, Bernd Sturmfels and Marta Panizzut
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 30 vertices. Their number is 36297333. We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.