K3 polytopes and their quartic surfaces-Reference-Cited by-同舟云学术

K3 polytopes and their quartic surfaces

Published:2021-01-01 Issue:1 Volume:21 Page:85-98
ISSN:1615-7168
Container-title:Advances in Geometry
language:en
Short-container-title:

Author:

Balletti Gabriele¹,Panizzut Marta²,Sturmfels Bernd³⁴

Affiliation:

1. Stockholm University , Stockholm Sweden

2. TU Berlin , Berlin Germany

3. MPI Leipzig , Leipzig Germany

4. UC Berkeley , Berkeley USA

Abstract

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 30 vertices. Their number is 36 297 333. We study the singular loci of quartic surfaces that tropicalize to K3 polytopes. These surfaces are stable in the sense of Geometric Invariant Theory.

Publisher

Walter de Gruyter GmbH

Subject

Geometry and Topology

Link

https://www.degruyter.com/document/doi/10.1515/advgeom-2020-0016/pdf

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