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Pré-Publication, Document De Travail Année : 2014

Representations of quasiprojective groups, Flat connections and Transversely projective foliations

Résumé

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 quasiprojective manifolds by dropping the hypothesis of quasi-unipotency at infinity. Secondly we establish an analogue classification for rank 2 flat meromorphic connections. In particular, we prove that a rank 2 flat meromorphic connection with irregular singularities having non trivial Stokes projectively factors through a connection over a curve.
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Dates et versions

hal-00942861 , version 1 (06-02-2014)
hal-00942861 , version 2 (16-10-2015)
hal-00942861 , version 3 (04-07-2016)

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Frank Loray, Frédéric Touzet, Jorge Vitorio Pereira. Representations of quasiprojective groups, Flat connections and Transversely projective foliations. 2014. ⟨hal-00942861v1⟩
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