On Deformations of Kähler Manifolds with Non Vanishing Holomorphic Vector Fields

نویسندگان

  • J. AMORÓS
  • M. MANJARÍN
چکیده

In this article we study compact Kähler manifolds admitting nonsingular holomorphic vector fields with the aim of extending to this setting the classical birational classification of projective varieties with tangent vector fields. We introduce and analyze a particular type of deformations, that we call tangential deformations, and we prove that each compact Kähler manifold X with nowhere vanishing vector fields admits an arbitrarily small tangential deformation which is a suspension over a torus; that is, a quotient of F × Cs fibering over a torus T = Cs/Λ. We derive some results dealing with the structure of such manifolds and, in particular, we prove an extension to Kähler manifolds of the so-called Calabi’s Second Conjecture. We also show that, up to a finite covering, X is deformation of a product F × T where F is a Kähler manifold without non-singular vector fields and T is a torus. A complete classification when X is a projective manifold or when dimX ≤ s + 2 is also given.

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تاریخ انتشار 2009