Involutive varieties with smooth support
type: Item
instance of: scholarly article
title: Involutive varieties with smooth support
zbMATH Open document ID: 0879.32010
author: S. C. Coutinho
author: Daniel Levcovitz
published in: Journal of Algebra
publication date: 1998-01-04T00:00:00Z
review text: Let \(X\) be a smooth complex algebraic variety and \(\mathcal D_X\) be its sheaf of rings of differential operators. If \(\mathcal M\) is a coherent sheaf of modules over \(\mathcal D_X\) then its characteristic variety Ch\((\mathcal M)\) is a subvariety of the cotangent bundle \({\text T}^{\star}X.\) A structure theorem for conic involutive varieties of the cotangent bundle of a smooth algebraic variety \(W\) whose projection \(\pi(W)\) on \(X\) is smooth is proved. Let \(W\) be a conical involutive irreducible subvariety of \({\text T}^{\star}X\) and \(\pi(W)\subseteq Y,\) where \(Y\) is a smooth hypersurface of \(X.\) Denote by \(\rho:{\text T}^{\star}X|_Y\to{\text T}^{\star}Y\) the natural projection. Then \(\rho(W)\) is a conical involutive irreducible subvariety of \({\text T}^{\star}Y,\) \(\rho^{-1}(\rho(W))=W\) and \(\dim \rho(W)=\dim W -1.\) The paper includes an example of a conic involutive variety of \(\text{T}^{\star}X\) which is not the characteristic variety of any \(\mathcal D_X\)-module.
Mathematics Subject Classification ID: 32C38
Mathematics Subject Classification ID: 14F10
zbMATH DE Number: 1026087
zbMATH Keywords: sheaves of differential operators and their modules
zbMATH Keywords: characteristic varieties
zbMATH Keywords: conic involutive varieties of the cotangent bundle
MaRDI profile type: Publication
full work available at URL: jabr.1996.6934
OpenAlex ID: W1999737130
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DOI: 10.1006/JABR.1996.6934
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description: scientific article; zbMATH DE number 1026087