Bounds for degrees of syzygies of polynomials defining a grade two ideal

2020/12/15 by Teresa Cortadellas Benítez, Benitez, Teresa Cortadellas, Carlos D’Andrea +3
Computer Science · Mathematics · #13D02 #13P20 #14Q20 #68W30 #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2012.08137

openalex publication_date 2020/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We make explicit the exponential bound on the degrees of the polynomials appearing in the Effective Quillen-Suslin Theorem, and apply it jointly with the Hilbert-Burch Theorem to show that the syzygy module of a sequence of m polynomials in n variables defining a complete intersection ideal of grade two is free, and that a basis of it can be computed with bounded degrees. In the known cases, these bounds improve previous results.

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