IJPAM: Volume 37, No. 1 (2007)

HOMOGENEOUS VECTOR BUNDLES ON
QUADRIC HYPERSURFACES

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 such that $n \ge 2$ and $-1 \le s \le n-1$ . Let $Q_{n,s} \subset {\bf {P}}^{n+1}$ be an -dimensional quadric hypersurface such that $\dim (\mbox{Sing}(Q_{n,s})) = s$ . Let be a vector bundle on $Q_{n,s}$ such that $H^1(Q_{n,s},{\text{\rm End}}(E)(-1)) = 0$ . Here we use a proof by N. Mohar Kumar to show that $g^\ast (E) \cong E$ for all $g\in \mbox{Aut}^0(Q_{n,s})$ .