C-对的Albanese映射
代数几何
2024-11-12 v2 复变函数
摘要
本文着眼于双曲性、有理点和整曲线等应用，探讨了在Campana的C-对（或“几何轨形”）理论中构造Albanese映射的问题。本文引入了C-半环对作为经典Albanese理论中使用的（半）环的类比，并遵循Serre的方法，将C-对的Albanese映射定义为到C-半环对的泛映射。本文证明了Albanese映射在相关情形下存在，给出了精确的存在性判据，并猜想“弱Albanese映射”是无条件存在的。
引用
@article{arxiv.2410.00405,
title = {The Albanese of a C-pair},
author = {Stefan Kebekus and Erwan Rousseau},
journal= {arXiv preprint arXiv:2410.00405},
year = {2024}
}
备注
Version 2: Fix cross-references between the papers arXiv:2407.10668, arXiv:2410.01245, and arXiv:2410.00405. Add an example highlighting differences between various notions of irregularity. Add a brief appendix on the simplicity of general Prym varieties