Curves on the product of two $K-$trivial surfaces

TL;DR

This paper investigates the properties of curves on the product of two K-trivial surfaces, establishing that the minimal genus of a non-trivial curve on the product of two very general abelian surfaces is 6.

Contribution

It provides a new result determining the minimal genus of non-trivial curves on the product of two very general abelian surfaces.

Findings

Minimal genus of non-trivial curves on A_1×A_2 is 6.

Focus on the product of two very general abelian surfaces.

Study of curves on K-trivial surface products.

Abstract

We study curves on the product of two $K$-trivial surfaces. In the case of the product of two very general abelian surfaces $A_1\times A_2$, we prove that the minimal genus of a non-trivial curve on $A_1\times A_2$ is $6$.