Year: 2025
Type: preprint
Abstract: We consider classes of codimension two Cohen--Macaulay ideals over a standard graded polynomial ring over a field. We revisit Vasconcelos' problem on $3\times 2$ 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 Tohǎneanu. 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 $G_d$ condition of Artin--Nagata.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414900328
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