Let \$E\$ be an indecomposable rank two vector bundle on the projective space \$\PP^n, n \ge 3\$, over an algebraically closed field of characteristic zero. It is well known that \$E\$ is arithmetically Buchsbaum if and only if \$n=3\$ and \$E\$ is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface \$Q_n\subset\PP^{n+1}\$, \$n\ge 3\$. We give in fact a full classification and prove that \$n\$ must be at most \$5\$. As to \$k\$-Buchsbaum rank two vector bundles on \$Q_3\$, \$k\ge2\$, we prove two boundedness results.

### On Buchsbaum bundles on quadric hypersurfaces

#### Abstract

Let \$E\$ be an indecomposable rank two vector bundle on the projective space \$\PP^n, n \ge 3\$, over an algebraically closed field of characteristic zero. It is well known that \$E\$ is arithmetically Buchsbaum if and only if \$n=3\$ and \$E\$ is a null-correlation bundle. In the present paper we establish an analogous result for rank two indecomposable arithmetically Buchsbaum vector bundles on the smooth quadric hypersurface \$Q_n\subset\PP^{n+1}\$, \$n\ge 3\$. We give in fact a full classification and prove that \$n\$ must be at most \$5\$. As to \$k\$-Buchsbaum rank two vector bundles on \$Q_3\$, \$k\ge2\$, we prove two boundedness results.
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2012
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http://arxiv.org/abs/1108.0075
Arithmetically Buchsbaum rank two vector bundles, smooth quadric hypersurfaces
E. Ballico; F. Malaspina; P. Valabrega; M. Valenzano
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/2318/93911`