English

Degenerations of scrolls to unions of planes

Algebraic Geometry 2007-05-23 v2

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 gg and of degree dd larger than 2g+42g+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.

Keywords

Cite

@article{arxiv.math/0601295,
  title  = {Degenerations of scrolls to unions of planes},
  author = {Alberto Calabri and Ciro Ciliberto and Flaminio Flamini and Rick Miranda},
  journal= {arXiv preprint arXiv:math/0601295},
  year   = {2007}
}

Comments

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