The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid
Quantum Algebra
2026-05-19 v1 Commutative Algebra
Rings and Algebras
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.
Cite
@article{arxiv.2605.18568,
title = {The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid},
author = {Myriam Mahaman},
journal= {arXiv preprint arXiv:2605.18568},
year = {2026}
}