JournalsrlmVol. 17, No. 2pp. 95–123

Degenerations of scrolls to unions of planes

  • Ciro Ciliberto

    Università di Roma, Italy
  • Alberto Calabri

    Università di Ferrara, Italy
  • Flaminio Flamini

    Università di Roma Tor Vergata, Italy
  • Rick Miranda

    Colorado State University, Fort Collins, United States
Degenerations of scrolls to unions of planes cover


In this paper we study degenerations of scrolls to union of planes, a problem already considered by G. Zappa in \cite{Zap1} and \cite{Zap2}. 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 gg and of degree d2g+4d \geq 2g+4 in \Ppd2g+1\Pp^{d-2g+1}. We also study properties of components of the Hilbert scheme parametrizing scrolls. Finally we review Zappa's original approach.

Cite this article

Ciro Ciliberto, Alberto Calabri, Flaminio Flamini, Rick Miranda, Degenerations of scrolls to unions of planes. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 17 (2006), no. 2, pp. 95–123

DOI 10.4171/RLM/457