Hypersurfaces quasi-invariant by codimension one foliations
Copyright policy )Hypersurfaces quasi-invariant by codimension one foliations
Abstract We present a variant of the classical Darboux-Jouanolou Theorem. Our main result provides a characterization of foliations which are pull-backs of foliations on surfaces by rational maps. As an application, we provide a structure theorem for foliations on 3-folds admitting an infinite number of extremal rays.
Darboux-Jouanolou theorem, Dynamical Systems (math.DS), 510, Mathematics - Algebraic Geometry, rational maps, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Foliations (differential geometric aspects), FOS: Mathematics, Foliations in differential topology; geometric theory, Dynamical aspects of holomorphic foliations and vector fields, Mathematics - Dynamical Systems, Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG), foliations
Darboux-Jouanolou theorem, Dynamical Systems (math.DS), 510, Mathematics - Algebraic Geometry, rational maps, Complex vector fields, holomorphic foliations, \(\mathbb{C}\)-actions, Foliations (differential geometric aspects), FOS: Mathematics, Foliations in differential topology; geometric theory, Dynamical aspects of holomorphic foliations and vector fields, Mathematics - Dynamical Systems, Minimal model program (Mori theory, extremal rays), Algebraic Geometry (math.AG), foliations
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