Construction of Vector Fields and Riccati Foliations Associated to Groups of Projective Automorphisms
نویسنده
چکیده
Our main result states that given a finitely generated subgroup G of Aut(CP (2)), there is an algebraic foliation F on a complex projective 3-manifold M3 with a bundle structure over CP (1) and fiber CP (2), such that F is transverse to almost every fiber of the bundle and with global holonomy conjugate to G.
منابع مشابه
Vector fields and foliations associated to groups of projective automorphisms
We introduce and give normal forms for (one-dimensional) Riccati foliations (vector fields) on C×CP (2) and C×Cn. These are foliations are characterized by transversality with the generic fiber of the first projection and we prove they are conjugate in some invariant Zariski open subset to the suspension of a group of automorphisms of the fiber, CP (2) or C n , this group called global holonomy...
متن کاملOn holomorphic foliations with projective transverse structure
We study codimension one holomorphic foliations on complex projective spaces and compact manifolds under the assumption that the foliation has a projective transverse structure in the complement of some invariant codimension one analytic subset. The basic motivation is the characterization of pull-backs of Riccati foliations on projective spaces. Our techniques apply to give a description of th...
متن کاملOD-characterization of $U_3(9)$ and its group of automorphisms
Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.
متن کاملOn the Integrability of Polynomial Fields in the Plane by Means of Picard-vessiot Theory
We study the integrability of polynomial vector fields using Galois theory of linear differential equations when the associated foliations is reduced to a Riccati type foliation. In particular we obtain integrability results for some families of quadratic vector fields, Liénard equations and equations related with special functions such as Hypergeometric and Heun ones. We also study the Poincar...
متن کاملGeneralized Transversely Projective Structure on a Transversely Holomorphic Foliation
The results of Biswas (2000) are extended to the situation of transversely projective foliations. In particular, it is shown that a transversely holomorphic foliation defined using everywhere locally nondegenerate maps to a projective space CPn, and whose transition functions are given by automorphisms of the projective space, has a canonical transversely projective structure. Such a foliation ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010