English

Harbourne constants, pull-back clusters and ramified morphisms

Algebraic Geometry 2022-08-23 v2

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 HH-index arbitarily close to 25/73.571-25/7\simeq -3.571, smaller than any previously known result.

Keywords

Cite

@article{arxiv.1810.03926,
  title  = {Harbourne constants, pull-back clusters and ramified morphisms},
  author = {Piotr Pokora and Joaquim Roé},
  journal= {arXiv preprint arXiv:1810.03926},
  year   = {2022}
}

Comments

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

R2 v1 2026-06-23T04:33:18.031Z