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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-2,
author = {Tomasz Maszczyk},
title = {One-dimensional infinitesimal-birational duality through differential operators},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {23-43},
zbl = {1172.16307},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-2}
}
Tomasz Maszczyk. One-dimensional infinitesimal-birational duality through differential operators. Fundamenta Mathematicae, Tome 189 (2006) pp. 23-43. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm191-1-2/