English

Negative curves on special rational surfaces

Algebraic Geometry 2020-04-28 v2

Abstract

We study negative curves on surfaces obtained by blowing up special configurations of points in the complex projective palne. Our main results concern the following configurations: very general points on a cubic, 3-torsion points on an elliptic curve and nine Fermat points. As a consequence of our analysis, we also show that the Bounded Negativity Conjecture holds for the surfaces we consider. The note contains also some problems for future attention.

Keywords

Cite

@article{arxiv.1909.05899,
  title  = {Negative curves on special rational surfaces},
  author = {Marcin Dumnicki and Lucja Farnik and Krishna Hanumanthu and Grzegorz Malara and Tomasz Szemberg and Justyna Szpond and Halszka Tutaj-Gasinska},
  journal= {arXiv preprint arXiv:1909.05899},
  year   = {2020}
}

Comments

11 pages, v.2 13 pages, major revision

R2 v1 2026-06-23T11:13:56.649Z