Rational Curves on Quasi-Projective Surfaces

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.

159 pages

References in corpus (1)

• Boundedness theorem for Fano log-threefolds

Cited by in corpus (6)

• Square-tiled surfaces and rigid curves on moduli spaces
• Del Pezzo Surfaces in Weighted Projective Spaces
• Complements on surfaces
• Classification of Exceptional Complements: Elliptic Curve Case
• On extremal transitions of Calabi-Yau threefolds and the singularity of the associated 7-space from rolling
• Mori conic bundles with a reduced log terminal boundary