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Pré-Publication, Document De Travail Année : 2011

On the smooth locus of aligned Hilbert schemes: the k-secant lemma and the general projection theorem

Résumé

Let X be a smooth, connected, dimension n, quasi-projective variety imbedded in \PP_N. Consider integers {k_1,...,k_r}, with k_i>0, and the Hilbert Scheme H_{k_1,...,k_r}(X) of aligned, finite, degree \sum k_i, subschemes of X, with multiplicities k_i at points x_i (possibly coinciding). The expected dimension of H_{k_1,...,k_r}(X) is 2N-2+r-(\sum k_i)(N-n). We study the locus of points where H_{k_1,...,k_r}(X) is not smooth of expected dimension and we prove that the lines carrying this locus do not fill up \PP_N

Dates et versions

hal-00672120 , version 1 (20-02-2012)

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Laurent Gruson, Christian Peskine. On the smooth locus of aligned Hilbert schemes: the k-secant lemma and the general projection theorem. 2011. ⟨hal-00672120⟩
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