Degree bounds for Gröbner bases of low-dimensional polynomial ideals
Ernst W Mayr, Stephan Ritscher · 2010
Let K[X] be a ring of multivariate polynomials with coefficients in a field K, and let f1, ..., fs be polynomials with maximal total degree d which generate an ideal I of dimension r. Then, for every admissible ordering, the total degree of polynomials in a Grobner basis for I is bounded by 2 (1/2dn-r + d)2r. This is proved using the cone decompositions introduced by Dube in [5]. Also, a lower bound of similar form is given.