Abstract:

Poincare holonomy varieties (or SL(2, C)-opers) are half-dimensional symplectic slices in the PSL(2, C)-character varieties of surfaces. The vector space of holomorphic quadratic differentials on a Riemann surface corresponds to such a slice by the holonomy map of complex projective structures. We construct analuogues of such slices from the viewpoint of Thurston's parametrization of complex projective structures.