185 citations · 449 across the 32 of their papers we have counts for
4 papers · 1 filter
Counting curves on surfaces: a guide to new techniques and results
Lucia Caporaso
This is a survey describing recents developments in enumerative geometry of curves on projective varieties. Various methods to arrive at results such as Kontsevich's formula for pl…
Counting plane curves of any genus
Lucia Caporaso, Joe Harris
We obtain a recursive formula answering the following question: How many irreducible, plane curves of degree d and (geometric) genus g pass through 3d-1+g general points in the pla…
Parameter spaces for curves on surfaces and enumeration of rational curves
Lucia Caporaso, Joe Harris
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…
Enumerating curves on rational surfaces: the rational fibration method
Lucia Caporaso, Joe Harris
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…