TRANSVERSELY PROJECTIVE FOLIATIONS ON SURFACES: EXISTENCE OF MINIMAL FORM AND PRESCRIPTION OF MONODROMY

DOI10.1142/S0129167X07004278zbMath1124.37028arXivmath/0512397OpenAlexW2137196832MaRDI QIDQ5297765

Jorge Vitório Pereira, Frank Loray

Publication date: 13 July 2007

Published in: International Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512397

zbMATH Keywords

invariantsfoliationbirational geometrytransverse structure

Mathematics Subject Classification ID

Singularities of holomorphic vector fields and foliations (32S65) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (13)

Foliations with isolated singularities on Hirzebruch surfaces ⋮ Branched projective structures with Fuchsian holonomy ⋮ Rational endomorphisms of codimension one holomorphic foliations ⋮ Singular foliations with trivial canonical class ⋮ Monodromies of projective structures on surface of finite-type ⋮ An example of a modular foliation deducted from an algebraic solution of Painlevé VI equation ⋮ Representations of quasi-projective groups, flat connections and transversely projective foliations ⋮ Projective representations of fundamental groups of quasiprojective varieties: a realization and a lifting result ⋮ Universal isomonodromic deformations of meromorphic rank 2 connections on curves ⋮ On elliptic modular foliations ⋮ On the Structure of Codimension 1 Foliations with Pseudoeffective Conormal Bundle ⋮ Stability of rank 2 vector bundles along isomonodromic deformations ⋮ Logarithmic affine structures, parallelizable \(d\)-webs and normal forms

Cites Work

• On the holonomy group of algebraic curves invariant by holomorphic foliations
• On nonlinear differential Galois theory
• Singular codimension one foliations, Galois groupoid and first integrals
• Special coordinate coverings of Riemann surfaces
• On the height of foliated surfaces with vanishing Kodaira dimension
• Fibrations, divisors and transcendental leaves

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