Moduli spaces of rank two ACM bundles on the Segre product of three projective lines
type: Item
instance of: scholarly article
title: Moduli spaces of rank two ACM bundles on the Segre product of three projective lines
zbMATH Open document ID: 1332.14051
author: Gianfranco Casnati
author: Daniele Faenzi
author: Francesco Malaspina
published in: Journal of Pure and Applied Algebra
publication date: 2015-12-08T00:00:00Z
full work available at URL: https://arxiv.org/abs/1404.1188
full work available at URL: http://porto.polito.it/2627782/
review text: The authors describe the moduli space, denoted by \(\mathcal{M}(c_1,c_2)\), of indecomposable, initialized, ACM semistable bundles of rank 2, with first and second Chern classes denoted respectively by \(c_1\) and \(c_2\), on the Segre embedding of \(\mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1\) inside \(\mathbb{P}^7\). Its existence and irreducibility is proved; moreover, the authors describe the moduli space for each possible Chern class. The possible cases for first Chern classes for such bundles where given by the authors in [\textit{G. Casnati} et al., J. Algebra 429, 413--446 (2015; Zbl 1330.14072)]. In the present paper, for each one of the cases, the \(\mu\)-stability of the bundles is studied, and the possibilities for the second Chern classes are given explicitly.
reviewed by: Simone Marchesi
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14J45
Mathematics Subject Classification ID: 14D20
zbMATH DE Number: 6517760
zbMATH Keywords: ACM bundles
zbMATH Keywords: Del Pezzo threefold
MaRDI profile type: Publication
OpenAlex ID: W2963137344
arXiv ID: 1404.1188
cites work: A home-made Hartshorne-Serre correspondence
cites work: Vector bundles on fano 3-folds without intermediate cohomology
cites work: Moduli of vector bundles on the projective plane
cites work: Cohen-Macaulay modules on hypersurface singularities. II
cites work: ACM bundles on cubic surfaces
cites work: Stable Ulrich bundles
cites work: Rank two aCM bundles on the del Pezzo threefold with Picard number 3
cites work: On the genus and Hartshorne-Rao module of projective curves
cites work: The geometry of Ulrich bundles on del Pezzo surfaces
cites work: Q4522263
cites work: Resultants and Chow forms via exterior syzygies
cites work: The classification of homogeneous Cohen-Macaulay rings of finite representation type
cites work: Rank 2 arithmetically Cohen-Macaulay bundles on a nonsingular cubic surface
cites work: Even and odd instanton bundles on Fano threefolds of Picard number one
cites work: A smooth surface of tame representation type
cites work: Q3328651
cites work: Compact moduli spaces for slope-semistable sheaves
cites work: Varieties of small codimension in projective space
cites work: Q4143433
cites work: Q3579591
cites work: Q4220921
cites work: Q3313976
cites work: BIRATIONAL GEOMETRY OF MODULI VARIETIES OF VECTOR BUNDLES OVER $ \mathbf P^2$
cites work: Cohen-Macaulay modules on hypersurface singularities. I
cites work: Instanton bundles on Fano threefolds
cites work: An elementary proof of the rationality of the moduli space for rank 2 vector bundles on \({\mathbb{P}}^ 2\)
cites work: Horrocks correspondence on a quadric surface
cites work: On boundedness of families of torsion free sheaves
cites work: Q3788117
cites work: Vector bundles on complex projective spaces
cites work: Spinor Bundles on Quadrics
cites work: RANK 2 VECTOR BUNDLES OVER A COMPLEX QUADRIC SURFACE
cites work: Q4298328
DOI: 10.1016/J.JPAA.2015.09.018
description: scientific article