With D. Cerveau and A. Lins
Neto. To appear in Journal of Algebraic Geometry.
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As a consequence, the appendix has been replaced by these two references.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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