Unfolding of wild character varieties

Abstract

In this paper, we study wild character varieties on compact Riemann surfaces and construct Poisson maps from wild to tame character varieties by unfolding irregular singularities into regular ones. Furthermore, we show that these unfolding Poisson maps induce Poisson birational equivalences between wild and tame character varieties. This result provides an affirmative answer to a conjecture posed by Klimes, Paul, and Ramis.