The moduli of super-null correlation bundles on \({\mathbb P}_ 3\)
type: Item
instance of: scholarly article
title: The moduli of super-null correlation bundles on \({\mathbb P}_ 3\)
zbMATH Open document ID: 0596.14005
DOI: 10.1007/BF01450835
author: Valery K. Vedernikov
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164205
review text: Let \(M_ 2(c_ 1,c_ 2)\) denote the coarse moduli scheme of stable rank two vector bundles on \({\mathbb{P}}_ 3({\mathbb{C}})\) with fixed Chern classes. The paper is concerned with one particular component of \(M_ 2(0,c_ 2)\). Using only the properties of the spectrum of such bundles on \({\mathbb{P}}_ 3\) an irreducible, rational and generically nonsingular component is shown to exist in \(M_ 2(0,(k+1)^ 2)\). The general bundle of this component is the pull-back of a null-correlation bundle on \({\mathbb{P}}_ 3\) via the morphism of \({\mathbb{P}}_ 3\) onto \({\mathbb{P}}_ 3\) defined by the linear system of hyperplanes of degree \(k+1\) on the underlying \({\mathbb{P}}_ 3\). The method uses the general technique of reduction on unstable surfaces. The dimension of super-null-correlations component is \(8c_ 2-3+4h^ 0{\mathcal X}(-3)\), where \({\mathcal X}\) is the spectrum of type \({\mathcal X}^+=0^{k+1}1^ k...(k-1)^ 2k^ 1\) (positive part).
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14F05
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 3959612
zbMATH Keywords: coarse moduli scheme of stable rank two vector bundles
zbMATH Keywords: Chern classes
zbMATH Keywords: dimension of super-null-correlations component
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3959612