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

VALENZANO, Mario
2012-01-01

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.
2012
10
4
1361
1379
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
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