Resolutions of Differential Operators of Low Order for an Isolated Hypersurface Singularity
Abstract
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring R defining a surface in affine three-space over a field of characteristic zero. With this method, we construct an explicit minimal generating set for the modules of differential operators of order two and three, as well as their minimal free resolutions; this expands the results of Bernstein, Gel’fand, and Gel’fand and of Vigué. Our construction relies, in part, on a description of these modules that we derive in the singularity category of R. Namely, we build explicit matrix factorizations starting from that of the residue field.
Repository Citation
Diethorn, Rachel N., Jack Jeffries, Claudia Miller, et al. 2026. "Resolutions of Differential Operators of Low Order for an Isolated Hypersurface Singularity." Michigan Mathematical Journal 76(2): 261-337.
Publisher
University of Michigan Department of Mathematics
Publication Date
5-1-2026
Publication Title
Michigan Mathematical Journal
Department
Mathematics
Document Type
Article
DOI
http://dx.doi.org/10.1307/mmj/20236386
Language
English
Format
text
