Buchsbaum bundles on \(\mathbb{P}^n\)
type: Item
instance of: scholarly article
title: Buchsbaum bundles on \(\mathbb{P}^n\)
zbMATH Open document ID: 0971.14016
DOI: 10.1016/S0022-4049(99)00129-2
author: N. Mohan Kumar
author: Prabhakar A. Rao
published in: Journal of Pure and Applied Algebra
publication date: 2000-11-21T00:00:00Z
review text: A rank-two bundle on \(\mathbb{P}^n\) is said to be \(k\)-Buchsbaum if its first cohomology module is annihilated by the \(k\)-th power of the irrelevant ideal. Buchsbaum varieties of codimension two (in the sense of Chang) correspond to bundles which satisfy a stronger condition than 1-Buchsbaum (in fact, they have both all the intermediate cohomology modules and all the intermediate cohomology modules of all possible restrictions to linear subspaces 1-Buchsbaum). In this paper the authors show that there is no indecomposable rank two bundle on \(\mathbb{P}^n\) \((n>3)\) whose first cohomology module is 1-Buchsbaum (the case \(n=3\) -- the null-correlation bundle -- is well-known) and that there is no indecomposable rank two vector bundle on \(\mathbb{P}^n\) \((n>4)\) whose first cohomology module is 2-Buchsbaum [the case \(n=3\) was solved by \textit{Ph. Ellia} and \textit{A. Sarti}, in: ``Commuttaive algebra and algebraic geometry'', Proc. Ferrara Meeting Honor M. Fiorentini, Ferrara, Lect. Notes Pure Appl. Math. 206, 81-92 (1999; Zbl 0960.14026) and the case \(n=4\) is open].
reviewed by: Giorgio Bolondi
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14M10
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 1517300
zbMATH Keywords: Buchsbaum bundles
zbMATH Keywords: irrelevant ideal
MaRDI profile type: Publication
cites work: Characterization of arithmetically Buchsbaum subschemes of codimension 2 in \(\mathbb P^ n\)
cites work: An analogue of Max Noether's theorem
cites work: Q4263559
cites work: Stable vector bundles of rank 2 on \(P^ 3\)
cites work: A note on cohomology modules of rank two bundles
full work available at URL: s0022-4049(99)00129-2
OpenAlex ID: W2103032100
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description: scientific article; zbMATH DE number 1517300