In this paper we study degenerations of a scroll to a union of planes, a problem already considered by G. Zappa in the 1940s. We prove, using techniques different from the ones of Zappa, a degeneration result to a union of planes with the mildest possible singularities, for linearly normal scrolls of genus g and of degree d ≥ 2g+4 in P^(d-2g+1). We also study properties of components of the Hilbert scheme parametrizing scrolls. Finally we review Zappa's original approach.
Degenerations of scrolls to unions of planes
CALABRI, Alberto;
2006
Abstract
In this paper we study degenerations of a scroll to a union of planes, a problem already considered by G. Zappa in the 1940s. We prove, using techniques different from the ones of Zappa, a degeneration result to a union of planes with the mildest possible singularities, for linearly normal scrolls of genus g and of degree d ≥ 2g+4 in P^(d-2g+1). We also study properties of components of the Hilbert scheme parametrizing scrolls. Finally we review Zappa's original approach.File in questo prodotto:
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