Counting plane curves of any genus

1996/08/22 by Caporaso, Lucia, Harris, Joe · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9608025

Abstract

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 plane? The formula is proved by studying suitable degenerations of plane curves.

Cited by

• The Evolution of Enumerative Geometry: A Narrative from Classical Problems to Enriched Invariants

Related

• Completion of Katz-Qin-Ruan's Enumeration of Genus-Two Plane Curves
• Enumerative geometry of plane curves of low genus
• Counting curves on surfaces: a guide to new techniques and results
• Counting Plane Rational Curves: Old and New Approaches
• Enumeration of Genus-Three Plane Curves with a Fixed Complex Structure