Abstract
A holomorphic foliation with singularities in a complex manifold M , consists of a pair . 2 = ( , ~ , . Y ) , where the singular set ,~:Z is an analytic subset of M , and . 7 is a holomorphic foliation on M . ~ x . If the codimension of the foliation . 7 is one, and the codimension of the singular set $ 7 is at least 2, then, . Y may be represented by an equivalence class of holomorphic sections ~v of T*M | L, where L is a holomorphic line bundle, and ~v satisfies the Frobenius integrability condition w A dw = 0. If M is compact, the set Fo l (M, L) of those foliations represented by sections of T*M | L is an algebraic variety. The purpose of this paper, is to describe the deformations of logarithmic foliations, which are represented by sections of the type
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