Parameter spaces for curves on surfaces and enumeration of rational curves

Abstract

We answer some enumerative questions about irreducible rational curves on Hirzebruch surfaces, by combining an idea of Kontsevich with the study of the geometry of certain natural parameter spaces. Our formulas generalize Kontsevich's formula for rational plane curves of given degree.

77 pages, Tex type: AMSLaTex in LaTex 2.09 compatibility mode, figures are not included in the package, for a copy with pictures write to [email protected]

Cited by in corpus (5)

• Mirror Principle II
• Counting curves of any genus on rational ruled surfaces
• Counting plane curves of any genus
• The enumerative geometry of rational and elliptic curves in projective space
• Enumerating curves on rational surfaces: the rational fibration method