IJPAM: Volume 43, No. 3 (2008)

DOMINANT IRREDUCIBLE COMPONENTS OF
THE HILBERT SCHEMES OF SCROLLS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Fix integers $g \ge 4$ and $r \ge 2$. Let $H'[d,g,r]$ denote the open subset of $\mbox{\rm Hilb}({\bf {P}}^{d+r-rg-1})_{red}$ parametrizing the smooth $r$-dimensional and degree $d$ non-degenerate scrolls over a general smooth genus $g$ curve. Here we prove that if $d \ge r^2g+rg$ the algebraic set $H'[d,g,r]$ has at least $r$ irreducible components.

Received: January 7, 2008

AMS Subject Classification: 14H60, 14J26, 14N05

Key Words and Phrases: scroll, $r$-dimensional scroll, stable vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3