IJPAM: Volume 36, No. 3 (2007)

SYZYGY SHEAVES ON PROJECTIVE SPACES

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


Abstract.Fix a closed subscheme $Z \subset {\bf {P}}^N$ and a surjection

\begin{displaymath}\phi : \oplus _{i=1}^{m} \mathcal {O}_{{\bf {P}}^N}(-d_i)
\to \mathcal {I}_Z.\end{displaymath}

$\mbox{Ker}(F_\phi )$ is called a syzygy sheaf. Here we give a condition assuring that the vector bundle $\mbox{Ker}(F_\phi )\vert L$ is rigid for a general line $L \subset {\bf {P}}^N$.

Received: February 5, 2007

AMS Subject Classification: 14J60

Key Words and Phrases: syzygy sheaf, syzygy bundle, rigid vector bundle on ${\bf {P}}^1$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 3