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

MALASPINA, FRANCESCO;VALABREGA, Paolo;
2012

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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