Self-intersection Number of Negative Curves on Fermat Surfaces

TL;DR

This paper provides an explicit formula for the self-intersection number of negative curves on Fermat surfaces, aiming to address the Bounded Negativity Conjecture in this context.

Contribution

It introduces a new explicit formula for self-intersection numbers of negative curves on Fermat surfaces, offering insights into the Bounded Negativity Conjecture.

Findings

Derived an explicit formula for self-intersection numbers.

Provides evidence supporting or challenging the Bounded Negativity Conjecture.

Offers potential pathways for future proofs or disproofs.

Abstract

We give an explicit formula for the self-intersection number of negative curves on Fermat surfaces. The formula offers us hints to either prove or disprove the Bounded Negativity Conjecture for the Fermat surfaces.