PreprintCC BY 4.0arXiv
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.
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BibTeX
@misc{mahaman2026ring,
title = {{The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid}},
author = {Myriam Mahaman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.18568},
eprint = {2605.18568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.18568},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - The Ring of Differential Operators on a Nodal Curve is not a Bialgebroid
AU - Myriam Mahaman
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2605.18568
UR - https://arxiv.org/abs/2605.18568
AB - 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.
ER -