## Pull-back components of the space of holomorphic foliations on
CP(N), N at least 3.

With D. Cerveau and A. Lins
Neto. To appear in Journal of Algebraic Geometry.

### Summary

My contribution to this article was an Appendix, to be found in
various formats below. This appendix proves the following result.
Let $S$ be a complex analytic variety, with a given point~$s$.
Let $n\geq 1$ be an integer, and $X\to S$ be a smooth analytic family of
projective complex analytic varieties of dimension $d>0$,
embedded in $\PP^n_S:=\PP^n(\CC)\times S$. Suppose that the fibre $X_s$
at $s$ is a complete intersection. Then there is an open neighborhood
of $s$ in $S$ over which $X$ is a complete intersection.

As already written in the appendix, it was very probable that this
result is not new. In fact, the editor of the Journal of Algebraic
Geometry says that it can be found in ``Sernesi, E., Small
deformations of global complete
intersections. Boll. Un. Mat. Ital. (4) 12 (1975), no. 1-2,
138--146'', and in ``Catanese, F., Moduli of algebraic
surfaces. Theory of moduli (Montecatini Terme, 1985), 1--83, Lecture
Notes in Math., 1337, Springer, Berlin-New York, 1988''.

As a consequence, the appendix has been replaced by these two
references. It might be that the appendix can still be useful,
because it addresses exactly the cases needed in the article, and not
more (or less).

fichier DVI/DVI file (.dvi)
(7kB)

fichier PostScript non comprimé/uncompressed PostScript file (.ps)
(39kB)

fichier PDF non comprimé/uncompressed PDF file (.pdf)
(96kB)

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###### Dernière modification: 09 novembre 1999

edix@maths.univ-rennes1.fr