On the maximal number of du Val singularities for a K3 surface

TL;DR

This paper investigates the maximum number of disjoint nodal curves, specifically du Val singularities, that a K3 surface can have, establishing an upper bound of 16 in characteristic not equal to 2.

Contribution

It proves that a complex or algebraic K3 surface cannot have more than 16 disjoint du Val singularities, refining the understanding of their geometric constraints.

Findings

Maximum of 16 disjoint du Val singularities on K3 surfaces

Characteristic restrictions for the singularities

Enhanced understanding of K3 surface singularity configurations

Abstract

A complex K3 surface or an algebraic K3 surface in characteristics distinct from $2$ cannot have more than $16$ disjoint nodal curves.