2020/04/13 by Keller VandeBogert, VandeBogert, Keller
Computer Science · Mathematics · #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2004.06016
openalex publication_date 2020/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We produce a family of complexes called trimming complexes and explore\napplications. We study how trimming complexes can be used to deduce the Betti\ntable for the minimal free resolution of the ideal generated by subsets of a\ngenerating set for an arbitrary ideal I. In particular, we compute the Betti\ntable for removing an arbitrary generator from the ideal of submaximal\npfaffians of a generic skew symmetric matrix M. We also explicitly compute\nthe Betti table for the ideal generated by certain subsets of the generating\nset of the ideal of maximal minors of a generic n \× m matrix. Such\nideals are a subset of a class of ideals called determinantal facet ideals,\nwhose higher degree Betti numbers had not previously been computed.\n