arXiv math/06012952006-01-17math.AG

Degenerations of scrolls to unions of planes

Alberto Calabri, Ciro Ciliberto, Flaminio Flamini, Rick Miranda

备注：: Latex2e, 26 pages, 15 figures. submitted preprint. v.2: some misprints are corrected

英文摘要：

In this paper we study degenerations of scrolls to union of planes, a problem already considered by G. Zappa in 1940-50. We prove, using techniques different from the ones of Zappa, a degeneration result to union of planes with the mildest possible singularities, for linearly normal scrolls of genus $g$ and of degree $d$ larger than $2g+4$ in $\Pp^{d-2g+1}$. We also study properties of components of the Hilbert scheme parametrizing scrolls. Finally we review Zappa's original approach.

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