Deformations of locally complete intersections
Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 355-358.

Given a projective l.c.i. scheme, X N , we show that X has a smooth formal neighbourhood in which X is globally a complete intersection; that is, X is the intersection of codim(X) hypersurfaces.

Soit X un schéma projectif et localement intersection complète. On démontre qu'il existe un voisinage formel, X, de X, dans lequel X est une intersection complète globale ; c'est-à-dire que X est l'intersection de codim(X) hypersurfaces.

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DOI: 10.1016/S1631-073X(02)02490-1
Maclean, Catriona 1

1 Institut de mathématiques de Jussieu, Université Paris 6, 175, rue de Chevaleret, 75013, Paris, France
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Maclean, Catriona. Deformations of locally complete intersections. Comptes Rendus. Mathématique, Volume 335 (2002) no. 4, pp. 355-358. doi : 10.1016/S1631-073X(02)02490-1. http://www.numdam.org/articles/10.1016/S1631-073X(02)02490-1/

[1] R. Hartshorne, Algebraic Geometry, Grad. Texts in Math., Vol. 52, Springer

[2] A. Grothendieck, S.G.A., Facsimile 1, exposes 1–3, IHES, 1962

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