The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid

Abstract

In a previous article, we showed that local projectivity is a sufficient condition for the existence of a bialgebroid structure on the ring of differential operators on an affine variety. In this note, we show using elementary methods that the ring of differential operators on a nodal curve is neither locally projective nor does it admit a bialgebroid structure.

4 pages, minor corrections in Sec. 2 and affiliation added