Enumerating curves on rational surfaces: the rational fibration method
Lucia Caporaso, Joe Harris
Abstract
A new, simple method to approach enumerative questions about rational curves on rational surfaces is described. Applications include a short proof of Kontsevich's formula for plane curves and a the solution of the analogous problem for the Hirzebruch surface F3.
Create a lesson
Related papers
Complements on surfaces
V. V. Shokurov
Isolated rational curves on K3-fibered Calabi-Yau threefolds
Torsten Ekedahl, Trygve Johnsen, Dag Einar Sommervoll
Cohomology of complete intersections in toric varieties
Anvar R. Mavlyutov
The Gross-Kohnen-Zagier theorem in higher dimensions
Richard E. Borcherds
Real deformations and complex topology of plane curve singularities
Norbert A'Campo
Irreducibility of the moduli space of vector bundles on surfaces and Brill-Noether theory on singular curves
Tomas L. Gomez