Bounds for degrees of syzygies of polynomials defining a grade two ideal. (March 2023)

• Record Type: Journal Article
• Authors: Cortadellas Benítez, Teresa; D'Andrea, Carlos; Montoro, M. Eulàlia
• Is Part Of: Journal of symbolic computation. Volume 115(2023)
• Page Start: 124
• Page End: 141
• Publication Date: 2023-03
• Subjects: primary 13P20 -- secondary 13D02 14Q20 68W30; Effective Quillen-Suslin theorem -- Hilbert-Burch theorem -- Syzygyes -- μ-bases -- Degree bounds; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2022.08.004
• Languages: English
• ISSNs: 0747-7171

Abstract

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.