Towards the weighted bounded negativity conjecture for blow-ups of algebraic surfaces

TL;DR

This paper investigates a weighted version of the Bounded Negativity Conjecture for algebraic surfaces, providing bounds on self-intersection numbers, especially focusing on blow-ups which were previously less studied.

Contribution

It introduces bounds for self-intersection numbers of curves on blow-ups of algebraic surfaces, advancing understanding of the weighted bounded negativity conjecture.

Findings

Established bounds on self-intersection numbers for curves on blow-ups

Provided evidence supporting the weighted bounded negativity conjecture

Focused on a class of surfaces previously neglected in the conjecture

Abstract

In the present paper, we focus on a weighted version of the Bounded Negativity Conjecture which predicts that for every smooth projective surface in characteristic zero the self-intersection numbers of reduced and irreducible curves are bounded from below by a global constant. We gather evidence for this conjecture by showing various bounds on the self-intersection number of curves in an algebraic surface. We focus our attention on blow-ups of algebraic surfaces, which have so far been neglected.