Degenerations of scrolls to unions of planes

Details Degenerations of scrolls to unions of planes Degenerations of scrolls to unions of planes

2006-01-12

arxiv.org/abs/math/0601295v2

Mathematics

Algebraic Geometry

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

Scientific paper

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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