Foliations with vanishing Chern classes
نویسنده
چکیده
In this paper we aim at the description of foliations having tangent sheaf TF with c1(TF) = c2(TF) = 0 on non-uniruled projective manifolds. We prove that the universal covering of the ambient manifold splits as a product, and that the Zariski closure of a general leaf of F is an Abelian variety. It turns out that the analytic type of the Zariski closures of leaves may vary from leaf to leaf. We discuss how this variation is related to arithmetic properties of the tangent sheaf of the foliation.
منابع مشابه
D-bar Sparks
A ∂-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O-gerbes with connection, it yields a soft resolution of the sheaf O by currents on the man...
متن کاملD-bar Sparks, I
A ∂-analogue of differential characters for complex manifolds is introduced and studied using a new theory of homological spark complexes. Many essentially different spark complexes are shown to have isomorphic groups of spark classes. This has many consequences: It leads to an analytic representation of O ×-gerbes with connection, it yields a soft resolution of the sheaf O × by currents on the...
متن کاملD-bar Spark Theory and Deligne Cohomology
We study the Harvey-Lawson spark characters of level p on complex manifolds. Presenting Deligne cohomology classes by sparks of level p, we give an explicit analytic product formula for Deligne cohomology. We also define refined Chern classes in Deligne cohomology for holomorphic vector bundles over complex manifolds. Applications to algebraic cycles are given. A Bott-type vanishing theorem in ...
متن کاملChern characters via connections up to homotopy ∗
1 Introduction: The aim of this note is to point out that Chern characters can be computed using curvatures of " connections up to homotopy " , and to present an application to the vanishing theorem for Lie algebroids. Classically, Chern characters are computed with the help of a connection and its curvature. However, one often has to relax the notion of connection so that one gains more freedo...
متن کامل0 Chern characters via connections up to homotopy ∗
1 Introduction: The aim of this note is to point out that Chern characters can be computed using curvatures of " connections up to homotopy " , and to present an application to the vanishing theorem for Lie algebroids. Classically, Chern characters are computed with the help of a connection and its curvature. However, one often has to relax the notion of connection so that one gains more freedo...
متن کامل