One-dimensional infinitesimal-birational duality through differential operators
Volume 191 / 2006
Fundamenta Mathematicae 191 (2006), 23-43
MSC: Primary 16S32, 17B63; Secondary 16S30, 53D20.
DOI: 10.4064/fm191-1-2
Abstract
The structure of filtered algebras of Grothendieck's differential operators on a smooth fat point in a curve and graded Poisson algebras of their principal symbols is explicitly determined. A related infinitesimal-birational duality realized by a Springer type resolution of singularities and the Fourier transformation is presented. This algebro-geometrical duality is quantized in appropriate sense and its quantum origin is explained.
