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Degenerations of scrolls to unions of planes

Alberto Calabri·Ciro Ciliberto·Flaminio Flamini·Rick Miranda
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Abstract

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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BibTeXRIS

Alberto Calabri, Ciro Ciliberto, Flaminio Flamini, Rick Miranda. 2006-01-17. Degenerations of scrolls to unions of planes. https://arxiv.org/abs/math/0601295

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