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 / Ballico, E.; Malaspina, Francesco; Valabrega, Paolo; Valenzano, M.. - In: CENTRAL EUROPEAN JOURNAL OF MATHEMATICS. - ISSN 1895-1074. - 10:4(2012), pp. 1361-1379. [10.2478/s11533-012-0005-y]

### 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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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/2467985`
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