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arXiv · 2505.09623

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

Francesco Bastianelli·Ciro Ciliberto·Thomas Dedieu·Concettina Galati·Margherita Lelli-Chiesa·Edoardo Sernesi
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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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Francesco Bastianelli, Ciro Ciliberto, Thomas Dedieu, Concettina Galati, Margherita Lelli-Chiesa, Edoardo Sernesi. 2025-04-23. The Caporaso-Harris-Ran degeneration principle: proof and applications. https://arxiv.org/abs/2505.09623

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