Transverse deformations of holomorphic foliations. (English) Zbl 0607.32014

Gómez-Mont, Xavier

Algebraic geometry, Proc. Lefschetz Centen. Conf., Mexico City/Mex. 1984, Pt. I, Contemp. Math. 58, 127-139 (1986).

[For the entire collection see Zbl 0588.00015.]
The following moduli problem is studied. Given a holomorphic foliation in a compact complex manifold M, the author determines the number of complex structures which are compatible with the transversal structure of the foliation. As a result the author proves that the moduli depend only on the cohomology of the tangent bundle to the foliation. The paper concludes with an application to ruled surfaces.

Reviewer: M.Schottenloher

MSC:

32G05	Deformations of complex structures
32G13	Complex-analytic moduli problems
14D20	Algebraic moduli problems, moduli of vector bundles

Keywords:

holomorphic foliation in a complex manifold; deformations of holomorphic structure; moduli problem; transversal structure

Citations:

Zbl 0588.00015