Local negativity of surfaces with non-negative Koidara dimension and transversal configurations of curves

TL;DR

This paper establishes bounds on the negativity of configurations of smooth curves with transversal intersections on algebraic surfaces of non-negative Kodaira dimension, with specific results for line configurations on complete intersections.

Contribution

It provides new bounds on H-constants for curve configurations on certain algebraic surfaces, including a sharp bound for lines on complete intersections.

Findings

Bound on H-constants for transversal curve configurations

Sharp uniform bound for line configurations on complete intersections

Analysis of negativity properties on surfaces with non-negative Kodaira dimension

Abstract

We give a bound on the H-constants of configurations of smooth curves having transversal intersection points only on an algebraic surface of non-negative Kodaira dimension. We also study in detail configurations of lines on smooth complete intersections $X \subset \mathbb{P}^{n+2}_{\mathbb{C}}$ of multi-degree $d=(d_1, \dots, d_n)$, and we provide a sharp and uniform bound on their H-constants, which only depends on $d$.