Differential operators on toric varieties
type: Item
instance of: scholarly article
title: Differential operators on toric varieties
zbMATH Open document ID: 0824.14044
DOI: 10.1016/0022-4049(94)90064-7
author: Ian M. Musson
published in: Journal of Pure and Applied Algebra
publication date: 1995-11-16T00:00:00Z
review text: The author considers the surjectivity of the canonical map \(\theta : \mathbb{D} (Y)^ G \to \mathbb{D} (Y // G)\) where \(\mathbb{D} (Y // G)\) is the ring of differential operators on the quotient variety \(Y // G = \text{Spec} {\mathcal O} (Y)^ G\), \(G\) a reductive algebraic group and \(\mathbb{D} (Y)^ G\) the fixed ring. -- The author shows that if \(X\) is a toric variety then it is isomorphic to a quotient \(Y // G\) where \(G\) is a torus acting on an affine space \(K^ s\) and \(Y\) is a \(G\) invariant open subset of \(K^ s\). Then he shows that any ring of differential operators on \(X\) twisted by an invertible sheaf is a factor ring of the fixed ring \(D(Y)^ G\) by an ideal generated by central elements.
Mathematics Subject Classification ID: 14M25
Mathematics Subject Classification ID: 14M17
Mathematics Subject Classification ID: 13N10
zbMATH DE Number: 681810
zbMATH Keywords: fixed ring
zbMATH Keywords: toric variety
zbMATH Keywords: ring of differential operators
reviewed by: Rodolfo Salvi
MaRDI profile type: Publication
full work available at URL: 0022-4049(94)90064-7
OpenAlex ID: W1978538598
cites work: The topology of torus actions on symplectic manifolds. Transl. from the French by the author
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cites work: Q3313974
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cites work: Lifting differential operators from orbit spaces
cites work: Q3975997
description: scientific article; zbMATH DE number 681810