Work

Combinatorial K3 surfaces and the Mori fan of the Dolgachev–Nikulin–Voisin family in degree 2

Year: 2026

Type: article

Abstract: We introduce the notion of a combinatorial K3 surface. Those form a certain class of type III semistable K3 surfaces and are completely determined by combinatorial data called curve structures. Emphasis is put on degree 2 combinatorial K3 surfaces, but the approach can be used to study higher degree as well. We describe elementary modifications both in terms of the curve structures as well as on the Picard groups. Together with a description of the nef cone in terms of curve structures, this provides an approach to explicitly computing the Mori fan of the Dolgachev–Nikulin–Voisin family in degree 2.

Source: Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

DOI: 10.1007/s13366-025-00815-9

Authors: Klaus Hulek, Christian Lehn

Institutions: Leibniz University Hannover, Ruhr University Bochum

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Deutsche Forschungsgemeinschaft