2019/03/05 by Hanumanthu, Krishna, Subramaniam, Aditya
#14C17 #14C20 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1903.01729
Let X be a smooth projective surface and let C be an arrangement of curves on X. The Harbourne constant of C was defined as a way to investigate the occurrence of curves of negative self-intersection on blow ups of X. This is related to the bounded negativity conjecture which predicts that the self-intersection number of all reduced curves on a surface is bounded below by a constant. We consider a geometrically ruled surface X over a smooth curve and give lower bounds for the Harbourne constants of transversal arrangements of curves on X.