Action of the Cremona group on foliations on ℙℂ2: Some curious facts
-
Dominique Cerveau
und
Julie Déserti
Abstract
The Cremona group of birational transformations of ℙℂ2 acts on the space 𝔽(2) of holomorphic foliations on the complex projective plane. Since this action is not compatible with the natural graduation of 𝔽(2) by the degree, its description is complicated. The fixed points of the action are essentially described by Cantat and Favre in [J. Reine Angew. Math. 561 (2003), 199–235]. In that article we are interested in problems of “aberration of the degree”, that is, pairs
Funding source: Swiss National Science Foundation
Award Identifier / Grant number: PP00P2_128422/1
Funding source: ANR
Award Identifier / Grant number: ANR-11-JS01-004-01
We thank Alcides Lins Neto for helpful discussions, and the anonymous referee for remarks and suggestions.
© 2015 by De Gruyter
Artikel in diesem Heft
- Frontmatter
- Conjugacy classes of finite groups and graph regularity
- A note about complexity of lens spaces
- A note for alternating Ramanujan's circular summation formula
- On a question of Gillespie
- Jumping pairs of Steiner bundles
- On the recurrence of symmetric jump processes
- R-groups, elliptic representations, and parameters for GSpin groups
- The least common multiple of consecutive quadratic progression terms
- Hybrid bounds for quadratic Weyl sums and arithmetic applications
- Invariants of coinvariant algebras
- Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
- Distinction of the Steinberg representation II: An equality of characters
- Perturbations of functional inequalities for Lévy type Dirichlet forms
- Decomposable Leavitt path algebras for arbitrary graphs
- Group rings whose set of symmetric elements is Lie metabelian
- Heat kernel and Lipschitz–Besov spaces
- A case of monoidal uniqueness of algebraic models
- Schur tensor product of operator spaces
- On the upper bound for Bi(K)Bi(K*)
- Bredon cohomological dimensions for proper actions and Mackey functors
- Action of the Cremona group on foliations on ℙℂ2: Some curious facts
- Homological aspects of the dual Auslander transpose
- Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
- Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
Artikel in diesem Heft
- Frontmatter
- Conjugacy classes of finite groups and graph regularity
- A note about complexity of lens spaces
- A note for alternating Ramanujan's circular summation formula
- On a question of Gillespie
- Jumping pairs of Steiner bundles
- On the recurrence of symmetric jump processes
- R-groups, elliptic representations, and parameters for GSpin groups
- The least common multiple of consecutive quadratic progression terms
- Hybrid bounds for quadratic Weyl sums and arithmetic applications
- Invariants of coinvariant algebras
- Boundedness of certain singular integrals along surfaces on Triebel–Lizorkin spaces
- Distinction of the Steinberg representation II: An equality of characters
- Perturbations of functional inequalities for Lévy type Dirichlet forms
- Decomposable Leavitt path algebras for arbitrary graphs
- Group rings whose set of symmetric elements is Lie metabelian
- Heat kernel and Lipschitz–Besov spaces
- A case of monoidal uniqueness of algebraic models
- Schur tensor product of operator spaces
- On the upper bound for Bi(K)Bi(K*)
- Bredon cohomological dimensions for proper actions and Mackey functors
- Action of the Cremona group on foliations on ℙℂ2: Some curious facts
- Homological aspects of the dual Auslander transpose
- Nilpotent covers and non-nilpotent subsets of finite groups of Lie type
- Erratum to The distribution of the logarithm in an orthogonal and a symplectic family of L-functions [Forum Math. 26 (2014), 523–546]
