Differential operators on toric varieties
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.
scientific article; zbMATH DE number 681810
scientific article