L-valued 1-jet de Rham complexes and their induced spectral sequences
type: Item
instance of: scholarly article
title: L-valued 1-jet de Rham complexes and their induced spectral sequences
zbMATH Open document ID: 0715.58002
author: Takeshi Usa
published in: Journal of Mathematics of Kyoto University
publication date: 1990-01-01T00:00:00Z
review text: Let M be a compact, complex manifold, E a holomorphic vector bundle of rank r over M and \(L=Op(E)(1)\) the tautological line bundle of the projective bundle f: P(E)\(=(E^{\vee}-\{0\}/{\mathbb{C}}^*)\to M\). The author considers the sheaves of L-valued 1-jet forms on the projective bundle P(E) and makes them into a complex defining a suitable differential operator of first order by means of a global section of E. Then he constructs a double spectral sequence from ``E-valued'' cohomology, \(H^ p(M,\Omega^ p_ m(E))\) to topological cohomology of these complexes. The differential operator considered by the author is basically the one introduced by \textit{A. Ogus} in 1976 [Am. J. Math. 97(1975), 1085-1107 (1976; Zbl 0331.14002)].
Mathematics Subject Classification ID: 58A20
Mathematics Subject Classification ID: 58A12
Mathematics Subject Classification ID: 14F05
zbMATH DE Number: 4178146
zbMATH Keywords: de Rham complexes
zbMATH Keywords: sheaf cohomology
zbMATH Keywords: holomorphic vector bundle
zbMATH Keywords: double spectral sequence
reviewed by: Enrique Outerelo
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250520126
OpenAlex ID: W1604231731
DOI: 10.1215/KJM/1250520126
description: scientific article; zbMATH DE number 4178146