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Transversely affine foliations on projective manifolds

2014; International Press of Boston; Volume: 21; Issue: 5 Linguagem: Inglês

10.4310/mrl.2014.v21.n5.a5

ISSN

1945-001X

Autores

Gaël Cousin, Jorge Vitório Pereira,

Tópico(s)

Algebraic Geometry and Number Theory

Resumo

We describe the structure of singular transversely affine foliations of codimension one on projective manifolds with zero first Betti number.Our result can be rephrased as a theorem on rank two reducible flat meromorphic connections. 1 Introduction 986 2 Transversely affine foliations 988 2.1 Definition 988 2.2 Interpretation in terms of rational 1-forms 989 2.3 Singular divisor and residues 990 2.4 Examples and first properties 992 2.5 Holonomy 996 2.6 Transversely affine foliations as transversely projective foliations 997 3 Cohomology jumping loci for local systems 1001 3.1 Group cohomology 1001 3.2 Cohomology jumping loci for quasi-projective manifolds 1002 4 Factorization of representations 1003

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