Rank 2 arithmetically Cohen-Macaulay bundles on a nonsingular cubic surface
type: Item
instance of: scholarly article
title: Rank 2 arithmetically Cohen-Macaulay bundles on a nonsingular cubic surface
zbMATH Open document ID: 1133.14041
author: Daniele Faenzi
published in: Journal of Algebra
publication date: 2008-02-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0504492
review text: Let \((X,L)\) be a polarized projective variety. A vector bundle \(E\) on \(X\) is called arithmetically Cohen-Macaulay (or ACM for short) if \(H^i(X, E\otimes L^n)=0\) for all integers \(n\) and \(0<i<\dim X\). These bundles have been the focus of intense study. In this paper the author studies rank 2 ACM bundles on cubic hypersurfaces in projective 3-space. Like Lefschetz theorem for line bundles on hypersurfaces, rank two ACM bundles are rare in higher dimensions. But for hypersurfaces in \({\mathbb P}^3\), these are ubiquitous. The author classifies these vector bundles on cubic hypersurfaces.
reviewed by: N. Mohan Kumar
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14M05
zbMATH DE Number: 5235119
zbMATH Keywords: arithmetically Cohen-Macaulay vector bundles
zbMATH Keywords: cubic hypersurfaces
zbMATH Keywords: moduli spaces of bundles
zbMATH Keywords: Pfaffian
MaRDI profile type: Publication
OpenAlex ID: W1966805283
arXiv ID: math/0504492
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DOI: 10.1016/J.JALGEBRA.2007.10.005
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description: scientific article