Harbourne Constants, Pull-Back Clusters and Ramified Morphisms

Abstract

We describe the effect of ramified morphisms on Harbourne constants of reduced effective divisors. With this goal, we introduce the pullback of a weighted cluster of infinitely near points under a dominant morphism between surfaces, and describe some of its basic properties. As an application, we describe configurations of curves with transversal intersections and H-index arbitrarily close to - 25 / 7 ≃ - 3.571 , smaller than any previously known result.