Cohen--Macaulay ideals of codimension two and the geometry of plane points
Abstract
We consider classes of codimension two Cohen--Macaulay ideals over a standard graded polynomial ring over a field. We revisit Vasconcelos' problem on matrices with homogeneous entries and describe the homological details of Geramita's work on plane points. An additional topic is the homological discussion of minors fixing a submatrix in the context of a perfect codimension two ideal. A combinatorial outcome of the results is a proof of the conjecture on the Jacobian ideal of a hyperplane arrangement stated by Burity, Simis and Toh\v{a}neanu. The basic drive behind the present landscapes is a thorough analysis of the related Hilbert--Burch matrix, often without assuming equigeneration, linear presentation or even the popular condition of Artin--Nagata.
Cite
@article{arxiv.2503.03728,
title = {Cohen--Macaulay ideals of codimension two and the geometry of plane points},
author = {Dayane Lira and Geisa Oliveira and Zaqueu Ramos and Aron Simis},
journal= {arXiv preprint arXiv:2503.03728},
year = {2025}
}
Comments
Some improvements to the exposition have been made. arXiv admin note: text overlap with arXiv:2406.04266