具有不规则奇点的纯谱关系的仿射几何
复变函数
2025-10-08 v1 几何拓扑
摘要
纯谱关系 on the tangent bundle of a Riemann surface induces a complex affine structure on the complement of the poles. Local models for Fuchsian singularities are already known. In this paper, we introduce a complete set of local invariants for a meromorphic connection and provide local models for a complex affine structure in a punctured neighborhood of an irregular singularity. Generalizing a construction attributed to Veech, we introduce the Delaunay decomposition of a compact Riemann surface endowed with a meromorphic connection with irregular singularities. In particular, we give upper bounds on the complexity of the decomposition.
引用
@article{arxiv.2510.05677,
title = {The affine geometry of meromorphic connections with irregular singularities},
author = {Xavier Buff and Arnaud Chéritat and Guillaume Tahar},
journal= {arXiv preprint arXiv:2510.05677},
year = {2025}
}