Parameter spaces for curves on surfaces and enumeration of rational curves

1996/08/22 by Lucia Caporaso, Caporaso, Lucia, Joe Harris +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.alg-geom/9608024

openalex publication_date 1996/08/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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• Counting plane curves of any genus

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