The Caporaso-Harris-Ran degeneration principle: proof and applications

2025/04/23 by Francesco Bastianelli, Ciro Ciliberto, Bastianelli, Francesco +9
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Algebraic Geometry (math.AG) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2505.09623

openalex publication_date 2025/04/23 · openalex created_date 2025/10/15 · openalex updated_date 2026/07/28

Abstract

Severi varieties are the parameter spaces for curves with prescribed homology class and genus on a smooth surface. We describe their limits along degenerations of surfaces, with a view towards the enumeration of curves. This includes a complete proof of the Caporaso-Harris recursive formula, with all the necessary background on deformations of curves and singularities.

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