Towards bounded negativity of self-intersection on general blown-up projective planes

TL;DR

This paper investigates lower bounds for the self-intersection numbers of integral curves on blow-ups of the projective plane at general points, using deformation theory to establish bounds under certain conditions.

Contribution

It applies classical deformation theory to derive bounds on self-intersection numbers for curves with high ramification or low multiplicity on blown-up projective planes.

Findings

Established expected bounds for self-intersection in specific cases

Applied deformation theory to problems in algebraic geometry

Provided insights into the bounded negativity conjecture

Abstract

We address the problem of bounding from below the self-intersection of integral curves on the projective plane blown-up at general points. In particular, by applying classical deformation theory we obtain the expected bound in the case of either high ramification or low multiplicity.