Irreducible holonomy groups and first integrals for holomorphic foliations
-
Victor León
,
Mitchael Martelo
Abstract
We study groups of germs of complex diffeomorphisms having a property called irreducibility. The notion is motivated by the similar property of the fundamental group of the complement of an irreducible hypersurface in the complex projective space. Natural examples of such groups of germ maps are given by holonomy groups and monodromy groups of integrable systems (foliations) under certain conditions. We prove some finiteness results for these groups extending previous results in [D. Cerveau and F. Loray, Un théorème de Frobenius singulier via l’arithmétique élémentaire, J. Number Theory 68 1998, 2, 217–228]. Applications are given to the framework of germs of holomorphic foliations. We prove the existence of first integrals under certain irreducibility or more general conditions on the tangent cone of the foliation after a punctual blow-up.
References
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© 2021 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Approximating pointwise products of quasimodes
- On the group of a rational maximal bifix code
- Hörmander type multiplier theorems on bi-parameter anisotropic Hardy spaces
- Newton’s method for nonlinear stochastic wave equations
- On the classification of Schreier extensions of monoids with non-abelian kernel
- Smoothness filtration of the magnitude complex
- Varieties of nilpotent Lie superalgebras of dimension ≤ 5
- The Dual Baer Criterion for non-perfect rings
- Spectral property of the planar self-affine measures with three-element digit sets
- Spectral properties of certain Moran measures with consecutive and collinear digit sets
- Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space
- A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group
- Well-posedness of backward stochastic partial differential equations with Lyapunov condition
- Free division rings of fractions of crossed products of groups with Conradian left-orders
- Strong uncountable cofinality for unitary groups of von Neumann algebras
- Irreducible holonomy groups and first integrals for holomorphic foliations
- Alexandroff topologies and monoid actions
Artikel in diesem Heft
- Frontmatter
- Approximating pointwise products of quasimodes
- On the group of a rational maximal bifix code
- Hörmander type multiplier theorems on bi-parameter anisotropic Hardy spaces
- Newton’s method for nonlinear stochastic wave equations
- On the classification of Schreier extensions of monoids with non-abelian kernel
- Smoothness filtration of the magnitude complex
- Varieties of nilpotent Lie superalgebras of dimension ≤ 5
- The Dual Baer Criterion for non-perfect rings
- Spectral property of the planar self-affine measures with three-element digit sets
- Spectral properties of certain Moran measures with consecutive and collinear digit sets
- Envelopes of circles and spacelike curves in the Lorentz–Minkowski 3-space
- A polynomial bound for the number of maximal systems of imprimitivity of a finite transitive permutation group
- Well-posedness of backward stochastic partial differential equations with Lyapunov condition
- Free division rings of fractions of crossed products of groups with Conradian left-orders
- Strong uncountable cofinality for unitary groups of von Neumann algebras
- Irreducible holonomy groups and first integrals for holomorphic foliations
- Alexandroff topologies and monoid actions
