Differential operators on cones
type: Item
instance of: scholarly article
title: Differential operators on cones
zbMATH Open document ID: 0733.58045
DOI: 10.1215/S0012-7094-91-06301-5
author: Paul Burchard
published in: Duke Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: A linear system of partial differential equations on a complex manifold Y is a module over the ring \({\mathcal D}_ Y\) of holomorphic linear differential operators on Y. A theorem of Kashiwara states that \({\mathcal D}_ Y\)-modules supported on a submanifold Z are the same thing as \({\mathcal D}_ Z\)-modules. Because the analogue of this theorem may fail if Z is singular, Kashiwara has posed the problem of finding an appropriate Z-intrinsic characterization of the category of \({\mathcal D}_ Y\)-modules supported on singular Z. The aim of this paper is to give a partial answer to this question, namely: If Z is a cone, the existence of a spectral sequence for computing \({\mathcal D}_ Z\) is proved and then this result is applied when Y is a Riemann surface of genus greater than one or an Abelian variety.
Mathematics Subject Classification ID: 58J99
Mathematics Subject Classification ID: 32C38
zbMATH DE Number: 4213078
zbMATH Keywords: singular submanifold
zbMATH Keywords: ring of holomorphic linear differential operators
zbMATH Keywords: complex manifold
zbMATH Keywords: cone
reviewed by: I. Mihuţ
MaRDI profile type: Publication
cites work: DIFFERENTIAL OPERATORS ON A CUBIC CONE
cites work: Q5568131
cites work: Q5598869
cites work: Nakai's conjecture for invariant subrings
cites work: Q3708119
cites work: Introduction to the theory of analytic spaces
cites work: Differential Operators on an Affine Curve
cites work: Q5730918
full work available at URL: s0012-7094-91-06301-5
OpenAlex ID: W2083282779
description: scientific article; zbMATH DE number 4213078