English

Even sets of $(-4)$-curves on rational surface

Algebraic Geometry 2010-03-25 v1

Abstract

We study rational surfaces having an even set of disjoint (4)(-4)-curves. The properties of the surface SS obtained by considering the double cover branched on the even set are studied. It is shown, that contrarily to what happens for even sets of (2)(-2)-curves, the number of curves in an even set of (4)(-4)-curves is bounded (less or equal to 12). The surface SS has always Kodaira dimension bigger or equal to zero and the cases of Kodaira dimension zero and one are completely characterized. Several examples of this situation are given.

Keywords

Cite

@article{arxiv.1003.4648,
  title  = {Even sets of $(-4)$-curves on rational surface},
  author = {Maria Marti Sanchez},
  journal= {arXiv preprint arXiv:1003.4648},
  year   = {2010}
}

Comments

17 pages

R2 v1 2026-06-21T15:01:56.789Z