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We consider the space of ordered pairs of distinct $\mathbb{C}P^1$-structureson Riemann surfaces (of any orientations) which have identical holonomy, sothat the quasi-Fuchsian space is identified with a connected component of thisspace. This space holomorphically maps to the product of the Teichm\"ullerspaces minus its diagonal.  In this paper, we prove that this mapping is a complete local branchedcovering map. As a corollary, we reprove Bers' simultaneous uniformizationtheorem without any quasi-conformal deformation theory. Our main theorem isthat the intersection of arbitrary two Poincar\'e holonomy varieties (${\rmSL}_2\mathbb{C}$-opers) is a non-empty discrete set, which is closely relatedto the mapping.

Bers' simultaneous uniformization and the intersection of Poincare holonomy varieties