Moduli spaces of rank-2 ACM bundles on prime Fano threefolds
type: Item
instance of: scholarly article
title: Moduli spaces of rank-2 ACM bundles on prime Fano threefolds
zbMATH Open document ID: 1223.14047
author: Maria Chiara Brambilla
author: Daniele Faenzi
published in: Michigan Mathematical Journal
publication date: 2011-05-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/0806.2265
review text: A prime Fano threeefold \(X\) is a threefold whose Picard group is generated by an ample line bundle \(H\), and the canonical bundle \(K\) is equal to \(-H\). The authors study the existence of rank \(2\) vector bundles \(E\), over prime Fano threefolds, which are Arithmetically Cohen-Macaulay, i.e. their intermediate cohomology groups \(H^1E(nH)\) vanish, for all \(n\). After twisting by a multiple of \(H\), one can always assume that the first Chern class of \(E\) satisfies \(c_1(E)=0,H\). In this situation, the authors classify all possible second Chern classes that may occur. When \(c_1(E)=0\), the second Chern class is necessarily \(2\) or \(4\). When \(c_1(E)=H\), then \(c_2(E)\) can be either \(1\) or any number between \(1+g/2\) and \(g+3\) (\(g\) being the genus of \(X\)). The existence part, which is the most difficult, is achieved by starting with non locally free sheaves and using deformations. When \(c_1(E)=H\) and \(c_2(E)\neq 1+g/2\), the existence is only proved on threefolds \(X\) containing a line \(L\) with normal bundle equal to \(\mathcal O_L\oplus\mathcal O_L(-H)\).
reviewed by: Luca Chiantini
Mathematics Subject Classification ID: 14J60
Mathematics Subject Classification ID: 14J45
zbMATH DE Number: 5899027
zbMATH Keywords: Fano threefolds
MaRDI profile type: Publication
OpenAlex ID: W2015311077
arXiv ID: 0806.2265
cites work: Splitting criterion for reflexive sheaves
cites work: Compactifying the Picard scheme
cites work: Stability of Special Instanton Bundles on ℙ 2n + 1
cites work: A home-made Hartshorne-Serre correspondence
cites work: Vector bundles on fano 3-folds without intermediate cohomology
cites work: Vector bundles with no intermediate cohomology on Fano threefolds of type \(V_{22}\)
cites work: CURVES AND VECTOR BUNDLES ON QUARTIC THREEFOLDS
cites work: ON DEFORMATION OF SHEAVES
cites work: Variation der globalen Ext in Deformationen kompakter komplexer Räume
cites work: Variétés de Prym et jacobiennes intermédiaires
cites work: Determinantal hypersurfaces.
cites work: Q4428936
cites work: Q4027235
cites work: Vector bundles on Fano threefolds of genus 7 and Brill–Noether loci
cites work: Cohen-Macaulay modules on hypersurface singularities. II
cites work: Q4534511
cites work: Gorenstein biliaison and ACM sheaves
cites work: Rank 2 arithmetically Cohen-Macaulay bundles on a general quintic surface
cites work: On general surfaces defined by an almost linear Pfaffian
cites work: Q5699148
cites work: A SPLITTING CRITERION FOR RANK 2 BUNDLES ON A GENERAL SEXTIC THREEFOLD
cites work: Q4522263
cites work: The classification of homogeneous Cohen-Macaulay rings of finite representation type
cites work: Bundles over Fano threefolds of type \(V_{22}\)
cites work: Rank 2 arithmetically Cohen-Macaulay bundles on a nonsingular cubic surface
cites work: Q5595003
cites work: ON PRIME FANO THREEFOLDS OF GENUS 9
cites work: Q3362522
cites work: Rational points on quartics
cites work: Varieties of small codimension in projective space
cites work: Stable vector bundles of rank 2 on \(P^ 3\)
cites work: Stable reflexive sheaves
cites work: Generischer Spaltungstyp und zweite Chernklasse stabiler Vektorraumbündel vom Rang 4 auf \({\mathbb{P}}_ 4\)
cites work: Vector Bundles on the Punctured Spectrum of a Local Ring
cites work: Q3128810
cites work: Pfaffian lines and vector bundles on Fano threefolds of genus 8
cites work: Prime Fano threefolds and integrable systems
cites work: Cubic hypersurfaces and integrable systems
cites work: The Abel-Jacobi map for cubic threefold and periods of Fano threefolds of degree \(14\)
cites work: Quartic 3-fold: Pfaffians, vector bundles, and half-canonical curves
cites work: Elliptic curves and rank-2 vector bundles on the prime Fano threefold of genus 7
cites work: Parametrization of sing \(\Theta\) for a Fano 3-fold of genus 7 by moduli of vector
cites work: Geometry of the Lagrangian Grassmannian LG(3,6) with applications to Brill-Noether loci
cites work: Note on the representation spaces of O(2,1)
cites work: Q4193587
cites work: Q4220921
cites work: Cohen-Macaulay modules on hypersurface singularities. I
cites work: Rank-two vector bundles on general quartic hypersurfaces in \(\mathbb{P}^4\)
cites work: Q4815255
cites work: Q4694970
cites work: Q3745959
cites work: Multiple Structures on Smooth Support
cites work: Q4526675
cites work: Boundedness of semi-stable sheaves of small ranks
cites work: Arithmetically Cohen-Macaulay bundles on hypersurfaces
cites work: Arithmetically Cohen-Macaulay Bundles on Three Dimensisonal Hypersurfaces
cites work: Q5527561
cites work: Symplectic structure of the moduli space of sheaves on an abelian or K 3 surface
cites work: Q3478539
cites work: Biregular classification of Fano 3-folds and Fano manifolds of coindex 3
cites work: Curves and Symmetric Spaces, I
cites work: Q3041329

Moduli spaces of rank-2 ACM bundles on prime Fano threefolds (cites work)
cites work: Spinor Bundles on Quadrics

Moduli spaces of rank-2 ACM bundles on prime Fano threefolds (cites work)
cites work: Some extensions of Horrocks criterion to vector bundles on Grassmannians and quadrics

Moduli spaces of rank-2 ACM bundles on prime Fano threefolds (cites work)
cites work: Geometry and algebra of prime Fano 3-folds of genus 12.

Moduli spaces of rank-2 ACM bundles on prime Fano threefolds (DOI)
DOI: 10.1307/MMJ/1301586307