Degenerations of scrolls to unions of planes
Calabri, Alberto · Ciliberto, Ciro · Flamini, Flaminio · Miranda, Rick
Original · EN
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 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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