A twistor correspondence for homogeneous polynomial differential operators
type: Item
instance of: scholarly article
title: A twistor correspondence for homogeneous polynomial differential operators
zbMATH Open document ID: 0548.32016
DOI: 10.1007/BF01455931
published in: Mathematische Annalen
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164000
review text: In three and four dimensions solutions of certain linear differential equations are known to correspond to cohomology classes on complex manifolds known as 'twistor spaces'. In this paper such a twistor correspondence is established between solutions of differential operators on \({\mathbb{C}}^{n+1}\) for \(n>1\) of the form \(D=f(\partial /\partial x_ 1,\partial /\partial x_ 2,...,\partial /\partial x_{n+1})\), where f is a homogeneous polynomial of degree k, and certain cohomology classes on a twistor space Z. The space Z is the total space of the hyperplane bundle restricted to the subvariety of \({\mathbb{P}}_ n\) determined by the zeroes of the polynomial f. When 1\(\leq k\leq n\) this correspondence is shown to be an isomorphism.
Mathematics Subject Classification ID: 32K15
Mathematics Subject Classification ID: 58J99
Mathematics Subject Classification ID: 47F05
zbMATH DE Number: 3873704
zbMATH Keywords: homogeneous polynomial differential operators
zbMATH Keywords: cohomology classes on a twistor space
author: Michael K. Murray
MaRDI profile type: Publication
cites work: Homogeneous vector bundles
cites work: Q3961493
cites work: On the Relative De Rham Sequence
cites work: The generalized Penrose-Ward transform
cites work: Cohomology and massless fields
cites work: Q3961114
cites work: Q4143433
cites work: Linear field equations on self-dual spaces
cites work: Monopoles and geodesics
cites work: On the construction of monopoles
cites work: Vector bundles on complex projective spaces
cites work: Q5682517
OpenAlex ID: W2008240458
description: scientific article; zbMATH DE number 3873704