Harbourne Constants, Pull-Back Clusters and Ramified Morphisms

Piotr Pokora, Joaquim Roé

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Abstract

© 2019, The Author(s). 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.
Original languageEnglish
Article number109
Number of pages24
JournalResults in Mathematics
Volume74
Issue number3
DOIs
Publication statusPublished - 1 Sep 2019

Keywords

  • Algebraic curves
  • algebraic surfaces
  • blowups
  • clusters of points

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