Simultaneous Uniformization and Algebraic Correspondences

Mahan Mj, Sabyasachi Mukherjee

Published: 2024/9/16

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.