Representations of quasiprojective groups, Flat connections and Transversely projective foliations

2014/02/06 by Loray, Frank, Touzet, Frédéric, Pereira, Jorge Vitorio · 3 citations
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1402.1382

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.

Cited by

• Turbulent holomorphic foliations on compact complex tori and transversely holomorphic Cartan geometry
• Jets of flat partial connections II
• Density of integral points in the Betti moduli of quasi-projective varieties

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• Foliations on the moduli space of rank two connections on the projective line minus four points
• Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result
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