Harbourne constants and arrangements of lines on smooth hypersurfaces in $\mathbb{P}^3_{\mathbb{C}}$

TL;DR

This paper establishes bounds for global linear Harbourne constants associated with arrangements of lines on smooth hypersurfaces in complex projective three-space, contributing to the understanding of line configurations and their negativity properties.

Contribution

It provides new bounds for Harbourne constants specifically for line arrangements on smooth hypersurfaces in complex projective three-space.

Findings

Derived bounds for global linear Harbourne constants.

Enhanced understanding of line arrangements on smooth hypersurfaces.

Contributed to the theory of negativity in algebraic geometry.

Abstract

In this note we find a bound for the so-called global linear Harbourne constants for smooth hypersurfaces in $\mathbb{P}^{3}_{\mathbb{C}}$