2024/12/15 by Vaibhav Pandey, Pandey, Vaibhav, Matteo Varbaro +1
Mathematics · Physics and Astronomy · #13A30 #13A35 #13C40 #14M06 (Primary) 14M10 ( Secondary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #Graph theory and applications #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.2412.11235
openalex publication_date 2024/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let I be the ideal generated by the maximal minors of a matrix of indeterminates over a field and let J denote the generic link, i.e., the most general link, of I. The generators of the ideal J are not known. We provide an explicit description of the lead terms of the generators of J using Gröbner degeneration. Indeed, we construct a degeneration which preserves the entire graded Betti table of J on passing to the initial ideal. We leverage this construction to establish the equality of the symbolic and ordinary powers of J. Our analysis of the initial ideal readily yields the Gorenstein property of the associated graded ring of J, and, in positive characteristic, the F-rationality of the Rees algebra of J. Using the technique of F-split filtrations, we further obtain the F-regularity of the blowup algebras of J.