The complex symplectic geometry of the deformation space of complex projective structures. (English) Zbl 1318.53097
Summary: 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. Generalizations of results of C. McMullen are derived, notably quasifuchsian reciprocity. The symplectic geometry is also described in a Hamiltonian setting with the complex Fenchel-Nielsen coordinates on quasifuchsian space, recovering results of I. Platis.
MSC:
| 53D30 | Symplectic structures of moduli spaces |
Keywords:
complex projective structures; symplectic structures; Teichmüller theory; character variety; quasi-Fuchsian structuresReferences:
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