Towards the weighted bounded negativity conjecture for blow-ups of algebraic surfaces

Abstract

In the present paper, we focus on a weighted version of the Bounded Negativity Conjecture which predicts that for every smooth projective surface in characteristic zero the self-intersection numbers of reduced and irreducible curves are bounded from below by a global constant. We gather evidence for this conjecture by showing various bounds on the self-intersection number of curves in an algebraic surface. We focus our attention on blow-ups of algebraic surfaces, which have so far been neglected.

12 pages. This version incorporates referee's remarks

References in corpus (2)

• Bounded Negativity and Arrangements of Lines
• Local negativity of surfaces with non-negative Koidara dimension and transversal configurations of curves