Harbourne constants and conic configurations on the projective plane

TL;DR

This paper introduces Harbourne constants as a measure of bounded negativity on algebraic surfaces and estimates these constants specifically for conic configurations with transversal intersections on the complex projective plane.

Contribution

It provides the first estimation of Harbourne constants for conic configurations with transversal intersections on the complex projective plane.

Findings

Harbourne constants effectively measure bounded negativity.

Estimation of Harbourne constants for conic configurations.

Insights into negativity bounds on algebraic surfaces.

Abstract

In this note we exhibit the so-called Harbourne constants which capture and measure the Bounded Negativity on various birational models of an algebraic surface. We show an estimation for Harbourne constants for conic configurations on the complex projective plane with transversal intersection points.