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Representations of quasi-projective groups, flat connections and transversely projective foliations

2016; Volume: 3; Linguagem: Inglês

10.5802/jep.34

2429-7100

Frank Loray, Jorge Vitório Pereira, Frédéric Touzet,

Geometric Analysis and Curvature Flows

The main purpose of this paper is to provide a structure theorem for codimension-one singular transversely projective foliations on projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank-two representations of fundamental groups of quasi-projective manifolds by dropping the hypothesis of quasi-unipotency at infinity. Secondly we establish a similar classification for rank-two flat meromorphic connections. In particular, we prove that a rank-two flat meromorphic connection with irregular singularities having non trivial Stokes matrices projectively factors through a connection over a curve.