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.
L’objet de cet article est d’établir un théorème de structure pour les feuilletages singuliers transversalement projectifs de codimension sur une variété projective lisse. Pour ce faire, nous étendons d’abord la classification de Corlette et Simpson de représentations de rang des groupes fondamentaux des variétés quasi-projectives lisses en omettant l’hypothèse de quasi-unipotence à l’infini. Ensuite, nous établissons une classification analogue pour les connexions méromorphes plates de rang . En particulier, nous montrons qu’une connexion méromorphe plate de rang avec des singularités irrégulières et des matrices de Stokes non triviales se factorise par une connexion sur une courbe.
Accepted:
Published online:
DOI: 10.5802/jep.34
Keywords: Foliation, transverse structure, birational geometry, flat connections, irregular singular points, Stokes matrices
Mot clés : Feuilletage, structure transverse, géométrie birationnelle, connexion plate, points singuliers irréguliers, matrices de Stokes
@article{JEP_2016__3__263_0, author = {Loray, Frank and Pereira, Jorge Vit\'orio and Touzet, Fr\'ed\'eric}, title = {Representations of quasi-projective groups, flat connections and transversely~projective~foliations}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {263--308}, publisher = {ole polytechnique}, volume = {3}, year = {2016}, doi = {10.5802/jep.34}, mrnumber = {3522824}, zbl = {1353.37098}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jep.34/} }
TY - JOUR AU - Loray, Frank AU - Pereira, Jorge Vitório AU - Touzet, Frédéric TI - Representations of quasi-projective groups, flat connections and transversely projective foliations JO - Journal de l’École polytechnique — Mathématiques PY - 2016 SP - 263 EP - 308 VL - 3 PB - ole polytechnique UR - http://www.numdam.org/articles/10.5802/jep.34/ DO - 10.5802/jep.34 LA - en ID - JEP_2016__3__263_0 ER -
%0 Journal Article %A Loray, Frank %A Pereira, Jorge Vitório %A Touzet, Frédéric %T Representations of quasi-projective groups, flat connections and transversely projective foliations %J Journal de l’École polytechnique — Mathématiques %D 2016 %P 263-308 %V 3 %I ole polytechnique %U http://www.numdam.org/articles/10.5802/jep.34/ %R 10.5802/jep.34 %G en %F JEP_2016__3__263_0
Loray, Frank; Pereira, Jorge Vitório; Touzet, Frédéric. Representations of quasi-projective groups, flat connections and transversely projective foliations. Journal de l’École polytechnique — Mathématiques, Volume 3 (2016), pp. 263-308. doi : 10.5802/jep.34. http://www.numdam.org/articles/10.5802/jep.34/
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