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Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2016

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 foliationson projective manifolds. To reach our goal, we firstly extend Corlette-Simpson's classification of rank two representationsof fundamental groups of quasiprojective manifolds by dropping the hypothesis of quasi-unipotency at infinity.Secondly we establish an analogue classification for rank two flat meromorphic connections.In particular, we prove that a rank two flat meromorphic connection with irregular singularities having non trivial Stokesprojectively 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. Journal de l'École polytechnique — Mathématiques, 2016, 3, pp.263-308. ⟨10.5802/jep.34⟩. ⟨hal-00942861v3⟩
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