RMC - Vol. 12, Num. 1 - E. Ballico/L. Ramella

Full paper in PDF:
$%E. Ballico and L. Ramella, General stable bundles arising as normal bundles of projective curves, Rev. Mat. Complut. 12 (1999), no. 1, 17–26. %$

General Stable Bundles Arising as Normal Bundles of Projective Curves

Edoardo BALLICO and Luciana RAMELLA

Department of Mathematics University of Trento 38050 Povo (TN) — Italy ballico@science.unitn.it	Department of Mathematics University of Genova v. Dodecaneso 35 16146 Genova — Italy ramella@dima.unige.it

Received: September 9, 1998

ABSTRACT

Let $X$ be a smooth projective curve of genus $g ≥ 2$ . For all integers $r$ , $d$ with $r > 0$ let $M (X;r,δ)$ be the moduli scheme of rank $r$ stable vector bundles on $X$ with degree $δ$ .

Here we prove that for all integers $n$ , $d$ with $n ≥ 3$ and $2 d≥ (5n- 8)g+ 2n - 5n + 4$ there is an open dense subset $Ω$ of $M (X;n- 1,(n+ 1)d +2g - 2)$ such that for every $N ∈Ω$ there is a non-degenerate degree d embedding of $X$ in $ℙn$ with $N$ as normal bundle.

For the proof we use reducible smoothable curves.

1991 Mathematics Subject Classification: 14H10, 14H60, 14C05.