The monodromy groups of Schwarzian equations on closed Riemann surfaces

Details The monodromy groups of Schwarzian equations on closed Riemann surfaces The monodromy groups of Schwarzian equations on closed Riemann surfaces

1995-11-28

arxiv.org/abs/math/9511213v2

Ann. of Math. (2) 151 (2000), no. 2, 625-704

Mathematics

Complex Variables

80 pages, published version

Scientific paper

Let \theta:\pi_1(R) \to \PSL(2,\C) be a homomorphism of the fundamental group of an oriented, closed surface R of genus exceeding one. We will establish the following theorem. Theorem. Necessary and sufficient for \theta to be the monodromy representation associated with a complex projective stucture on R, either unbranched or with a single branch point of order 2, is that \theta(\pi_1(R)) be nonelementary. A branch point is required if and only if the representation \theta does not lift to \SL(2,\C).

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