Simultaneous Uniformization and Algebraic Correspondences
Geometric Topology
2025-09-23 v2 Complex Variables
Dynamical Systems
Abstract
We prove a generalization of Bers' simultaneous uniformization theorem in the world of algebraic correspondences. More precisely, we construct algebraic correspondences that simultaneously uniformize a pair of non-homeomorphic genus zero orbifolds. We also present a complex-analytic realization of the Teichm\"uller space of a punctured sphere in the space of correspondences.
Cite
@article{arxiv.2409.10468,
title = {Simultaneous Uniformization and Algebraic Correspondences},
author = {Mahan Mj and Sabyasachi Mukherjee},
journal= {arXiv preprint arXiv:2409.10468},
year = {2025}
}
Comments
The expository part of the article is based on arXiv:2103.00835, arXiv:2304.12699, and arXiv:2408.00204. To appear in Proceedings of Mathematical Society of Japan-SI conference on New Aspects of Teichm\"uller theory