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Dimension-Dependent Upper Bounds for Grobner Bases (1705.02776v1)
Published 8 May 2017 in cs.SC, math.AC, and math.AG
Abstract: We improve certain degree bounds for Grobner bases of polynomial ideals in generic position. We work exclusively in deterministically verifiable and achievable generic positions of a combinatorial nature, namely either strongly stable position or quasi stable position. Furthermore, we exhibit new dimension- (and depth-)dependent upper bounds for the Castelnuovo-Mumford regularity and the degrees of the elements of the reduced Grobner basis (w.r.t. the degree reverse lexicographical ordering) of a homogeneous ideal in these positions.