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 arbitarily close to $-25/7\simeq -3.571$, smaller than any previously known result.

arXiv comment27 pages, this is the final version incorporating referee's remarks, to appear in Results in Mathematics

References in corpus (4)

• Negative curves on algebraic surfaces
• Bounded Negativity and Arrangements of Lines
• Bounded negativity of self-intersection numbers of Shimura curves on Shimura surfaces
• The 21 reducible polars of Klein's quartic

Cited by in corpus (3)

• On $3$-syzygy and unexpected plane curves
• On the degree of curves with prescribed multiplicities and bounded negativity
• The cone of curves and the Cox ring of rational surfaces over Hirzebruch surfaces