Caporaso-Harris-Ran 退化原理：证明与应用
代数几何
2025-05-16 v1
摘要
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.
引用
@article{arxiv.2505.09623,
title = {The Caporaso-Harris-Ran degeneration principle: proof and applications},
author = {Francesco Bastianelli and Ciro Ciliberto and Thomas Dedieu and Concettina Galati and Margherita Lelli-Chiesa and Edoardo Sernesi},
journal= {arXiv preprint arXiv:2505.09623},
year = {2025}
}