English

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.

Keywords

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}
}