Simultaneous Uniformization and Algebraic Correspondences

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 Teichmüller space of a punctured sphere in the space of correspondences.

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 Teichmüller theory