Rational double points on supersingular K3 surfaces

TL;DR

This paper classifies all possible configurations of rational double points on supersingular K3 surfaces with Milnor number 21 and enumerates extremal elliptic fibrations on these surfaces.

Contribution

It provides a complete list of rational double point configurations and extremal elliptic fibrations on supersingular K3 surfaces, advancing the understanding of their geometric structures.

Findings

Complete classification of rational double point configurations with Milnor number 21.

Enumeration of all extremal (quasi-)elliptic fibrations on supersingular K3 surfaces.

Identification of possible configurations and fibrations on these surfaces.

Abstract

We investigate configurations of rational double points with the total Milnor number 21 on supersingular $K3$ surfaces. The complete list of possible configurations is given. As an application, we also give the complete list of extremal (quasi-)elliptic fibrations on supersingular $K3$ surfaces.