Counting elliptic fibrations on K3 surfaces

TL;DR

This paper develops a method to count jacobian elliptic fibrations on complex K3 surfaces up to automorphisms, providing explicit examples to demonstrate its effectiveness.

Contribution

It introduces a novel approach for counting elliptic fibrations on K3 surfaces and applies it to various explicit cases.

Findings

Successfully counts elliptic fibrations on K3 surfaces.

Provides explicit examples illustrating the counting method.

Advances understanding of elliptic fibrations on complex surfaces.

Abstract

We solve the problem of counting jacobian elliptic fibrations on an arbitrary complex projective K3 surface up to automorphisms. We then illustrate our method with several explicit examples.