The complex symplectic geometry of the deformation space of complex projective structures

Brice Loustau (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

This article investigates the complex symplectic geometry of the deformation space of complex projective structures on a closed oriented surface of genus at least 2. The cotangent symplectic structure given by the Schwarzian parametrization is studied carefully and compared to the Goldman symplectic structure on the character variety, clarifying and generalizing a theorem of S. Kawai [Kaw96]. Generalizations of results of C. McMullen are derived, notably quasi-Fuchsian reciprocity [McM00]. The symplectic geometry is also described in a Hamiltonian setting with the complex Fenchel-Nielsen coordinates on quasi-Fuchsian space, recovering results of I. Platis [Pla01].

Domaines: Géométrie différentielle [math.DG]; Géométrie symplectique [math.SG]

Brice Loustau. The complex symplectic geometry of the deformation space of complex projective structures. 2016. ⟨hal-01275182⟩