A hypergraph characterization of nearly complete intersections
Chiara Bondi, Courtney R. Gibbons, Yuye Ke, Spencer Martin, Shrunal, Pothagoni, Andrew Stelzer
TL;DR
This paper provides a comprehensive hypergraph-based characterization of nearly complete intersection ideals, extending previous work to arbitrary degrees and enabling the computation of minimal free resolutions from degree 2 data.
Contribution
It generalizes the characterization of nearly complete intersections to all generating degrees and introduces methods to compute their minimal free resolutions from degree 2 information.
Findings
Extended characterization to arbitrary degrees
Developed methods for minimal free resolution computation
Connected hypergraph theory with algebraic properties
Abstract
Recently, nearly complete intersection ideals were defined by Boocher and Seiner to establish lower bounds on Betti numbers for monomial ideals (arXiv:1706.09866). Stone and Miller then characterized nearly complete intersections using the theory of edge ideals (arXiv:2101.07901). We extend their work to fully characterize nearly complete intersections of arbitrary generating degrees and use this characterization to compute minimal free resolutions of nearly complete intersections from their degree 2 part.
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Taxonomy
TopicsCommutative Algebra and Its Applications · Polynomial and algebraic computation