Rational Curves on Quasi-Projective Surfaces

Details Rational Curves on Quasi-Projective Surfaces Rational Curves on Quasi-Projective Surfaces

1997-07-25

arxiv.org/abs/alg-geom/9707016v1

Mathematics

Algebraic Geometry

159 pages

Scientific paper

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.

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