The 3-divisibility of divisors on K3 surfaces in characteristic 3

TL;DR

This paper classifies 3-divisible configurations of rational curves on K3 surfaces in characteristic 3 and analyzes the resulting triple covers.

Contribution

It provides a complete classification of 3-divisible A_2^n configurations and their associated triple covers on K3 surfaces in characteristic 3.

Findings

Identified all possible 3-divisible A_2^n configurations

Classified the resulting triple covers comprehensively

Enhanced understanding of K3 surface configurations in characteristic 3

Abstract

We describe the possible 3-divisible $A_2^n$ configurations of smooth rational curves on K3 surfaces in characteristic 3 and fully classify the resulting triple covers.