English

Rational Curves on Quasi-Projective Surfaces

alg-geom 2008-02-03 v1 Algebraic Geometry

Abstract

The main result is that a quasi-projective surface has negative log Kodaira dimension (i.e. no log pluricanonical sections) iff it is dominated by images of the affine line. This follows from our main intermediate result, that the smooth locus of a log Fano surface is rationally connected. We also give a classification of all but a bounded family of rank one log del Pezzo surfaces.

Keywords

Cite

@article{arxiv.alg-geom/9707016,
  title  = {Rational Curves on Quasi-Projective Surfaces},
  author = {Sean Keel and James McKernan},
  journal= {arXiv preprint arXiv:alg-geom/9707016},
  year   = {2008}
}

Comments

159 pages

R2 v1 2026-07-22T07:42:44.118Z