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On the construction of some Buchsbaum varieties and the Hilbert scheme of elliptic scrolls in P^5

Dolores Bazan·Emilia Mezzetti
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Abstract

We study the degeneracy loci of general bundle morphisms from the direct sum of m copies of the structural sheaf on $P^n$ to $Ω(2)$, also from the point of view of the classical geometrical interpretation of the sections of $Ω(2)$ as linear line complexes. We consider in particular the case of $P^5$ with m=2, 3. For n=5 and m=3 we give an explicit description of the Hilbert scheme H of elliptic normal scrolls in $P^5$, by defining a natural rational map from the Grassmannian G(2,14) to H, which results to be dominant with general fibre of degree four.

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Dolores Bazan, Emilia Mezzetti. 2000-05-17. On the construction of some Buchsbaum varieties and the Hilbert scheme of elliptic scrolls in P^5. https://arxiv.org/abs/math/0005173

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