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arXiv · 1402.1382

Representations of quasiprojective groups, Flat connections and Transversely projective foliations

Frank Loray·Frédéric Touzet·Jorge Vitorio Pereira
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Abstract

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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Frank Loray, Frédéric Touzet, Jorge Vitorio Pereira. 2014-02-06. Representations of quasiprojective groups, Flat connections and Transversely projective foliations. https://arxiv.org/abs/1402.1382

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