Harbourne constants and arrangement

Harbourne constants and arrangements of lines on smooth hypersurfaces in P3C
Piotr Pokora
May 15, 2015
Abstract
In this note we find a bound for the so-called global linear Harbourne constants for smooth hypersur- faces in P3C
Keywords line configurations, Miyaoka inequality, blow-ups, negative curves, the Bounded Negativity Conjecture
Mathematics Subject Classification (2000) 14C20
1 Introduction
In this short note we find a global estimate for Harbourne constants which were introduced in [2] in order to capture and measure the Bounded Negativity on various birational models of an algebraic surface.
Definition 1.1. Let X be a smooth projective surface. We say that X has Bounded Negativity if there exists an integer b(X) such that for every reduced curve C ⊂ X one has the bound
C2