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

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.

20 pages, latex file. Revised version accepted for publication at the JSC Special Issue - ISSAC 2020