IJPAM: Volume 25, No. 3 (2005)


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

Abstract.Let $X$ be a smooth and connected projective curve of genus $g \ge 2$. Fix integers $k\ge 3$, $n_i>0$ and $d_i$, $1 \le i \le k$, and $r_i> 0$ and $a_i$, $1 \le i \le k-1$, such that $r_i+r_{i+1} = n_{i+1}$ for all $1 \le i \le k-2$, $n_1 > r_1$, $r_{k-1} < n_k$, $a_i+a_{i+1} = d_{i+1}$ for $1 \le i \le k-1$, $a_i/r_i < a_{i+1}/r_{i+1}$ for $1 \le i \le k-2$, $d_1/n_1 < a_1/r_1$. Then there is an exact sequence on $X$ such that all vector bundles $E_i$, $1 \le i \le k$, and $F_j:= \mbox{\rm Im}(f_j) = \mbox{\rm Ker}(f_{j+1})$, $1 \le j \le k-1$ are stable, $\mbox{\rm rank}(E_i)=n_i$, $\deg (E_i) = d_i$, $\mbox{\rm rank}(F_j) = r_j$ and $\deg (F_j) = a_j$ for all $i,j$. Furthermore, we may assume that each $F_j$, $1 \le j \le k-1$, is general in its moduli space of all stable vector bundles on $X$ with that degree and that rank.

Received: September 16, 2005

AMS Subject Classification: 14H60

Key Words and Phrases: stable vector bundle, vector bundles on curves, variety of complexes

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 25
Issue: 3