Toric foliations with split tangent sheaf
نویسندگان
چکیده
We study holomorphic foliations of arbitrary codimension in smooth complete toric varieties. show that split are stable if some good behaviour their singular set is provided. As an application these results, we exhibit irreducible components the space arise as pullbacks special T-invariant subvarieties.
منابع مشابه
Stability of Holomorphic Foliations with Split Tangent Sheaf
We show that the set of singular holomorphic foliations on projective spaces with split tangent sheaf and good singular set is open in the space of holomorphic foliations. We also give a cohomological criterion for the rigidity of holomorphic foliations induced by group actions and prove the existence of rigid codimension one foliations of degree n − 1 on P for every n ≥ 3.
متن کاملManifolds with Multiplication on the Tangent Sheaf
This talk reviews the current state of the theory of F–(super)manifolds (M, ◦), first defined in [HeMa] and further developed in [He], [Ma2], [Me1]. Here ◦ is an OM–bilinear multiplication on the tangent sheaf TM , satisfying an integrability condition. F–manifolds and compatible flat structures on them furnish a useful weakening of Dubrovin’s Frobenius structure which naturally arises in the q...
متن کاملVector Fields Tangent to Foliations
We investigate in this paper the topological stability of pairs (ω,X), where ω is a germ of an integrable 1-form and X is a germ of a vector field tangent to the foliation determined by ω.
متن کاملOn the Poincaré Problem for Foliations with Canonical Sheaf Defining a Morphism onto a Normal Surface
In this paper we reduce the Poincaré Problem for foliations in P to a problem of postulation of plane curves of degree m − 1, with m denoting the degree of the foliation. In the cases in which we can assure a solution for the Poincaré Problem the bound for the degree of the first integral depends only on the degree of the foliation. An intermediate result gives a solution for Painlevé’s Problem...
متن کاملA Hölder continuous vector field tangent to many foliations
We construct an example of a Hölder continuous vector field on the plane which is tangent to all foliations in a continuous family of pairwise distinct C foliations. Given any 1 ≤ r < ∞, the construction can be done in such a way that each leaf of each foliation is the graph of a Cr function from R to R. We also show the existence of a continuous vector field X on R and two foliations F and G o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Bulletin Des Sciences Mathematiques
سال: 2022
ISSN: ['0007-4497', '1952-4773']
DOI: https://doi.org/10.1016/j.bulsci.2022.103099