# Differential Isomorphism and Equivalence of Algebraic Varieties

@article{Berest2003DifferentialIA,
title={Differential Isomorphism and Equivalence of Algebraic Varieties},
author={Yuri Yu. Berest and George V. Wilson},
journal={arXiv: Algebraic Geometry},
year={2003}
}
• Published 22 April 2003
• Mathematics
• arXiv: Algebraic Geometry
In this survey article we discuss the question: to what extent is an algebraic variety determined by its ring of differential operators? In the case of affine curves, this question leads to a variety of mathematical notions such as the Weyl algebra, Calogero-Moser spaces and the adelic Grassmannian. We give a fairly detailed overview of this material.
18 Citations
• Mathematics
• 2008
. We show that Fourier transforms on the Weyl algebras have a geo-metric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of diﬀerential
• Mathematics
• 2007
Abstract.We show that Fourier transforms on the Weyl algebras have a geometric counterpart in the framework of toric varieties, namely they induce isomorphisms between twisted rings of differential
We give a natural cohomological interpretation of Letzter-Makar-Limanov invariants for rings of differential operators on algebraic curves.
• Mathematics
• 2004
We re-examine the bijective correspondence between the set of isomorphism classes of ideals of the first Weyl algebra and associated quiver varieties (Calogero-Moser spaces) \cite{BW1, BW2}. We give
• Mathematics
• 2011
We describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra $A_1(k)$. In particular, we give a geometric presentation for these groups in terms of
• Mathematics
• 2002
1.1. V-modules on singular varieties. Let Y denote a variety over a field and let Vy denote the full sheaf of differential operators on Y (in characteristic zero Vy is the familiar sheaf of
• Mathematics
Compositio Mathematica
• 2010
Abstract We introduce quasi-invariant polynomials for an arbitrary finite complex reflection group W. Unlike in the Coxeter case, the space of quasi-invariants of a given multiplicity is not, in
• Mathematics
• 2010
We describe the structure of the automorphism groups of algebras Morita equivalent to the first Weyl algebra $A_1$. In particular, we give a geometric presentation for these groups in terms of
• Mathematics
• 2007
The relations between these objects are well known and almost immediate. Thus, (1) is essentially the definition of (closed) points of HilbðCÞ. The bijection (1)! (2) is given by taking the quotient

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