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2023-03

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cc by (c) Teresa Cortadellas Benítez et al., 2023
Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/196304

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

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https://doi.org/10.1016/j.jsc.2022.08.004

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.

Subject

Àlgebra commutativa, Àlgebra homològica, Anells commutatius, Geometria algebraica, Algorismes computacionals

Subject (English)

Commutative algebra, Homological algebra, Commutative rings, Algebraic geometry, Computer algorithms

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citation

CORTADELLAS BENÍTEZ, Teresa, D'ANDREA, Carlos and MONTORO LÓPEZ, M. Eulàlia. Bounds for degrees of syzygies of polynomials defining a grade two ideal. Journal of Symbolic Computation. 2023. Vol. 115, num. 124-141. ISSN 0747-7171. [consulted: 11 of June of 2026]. Available at: https://hdl.handle.net/2445/196304

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