Dimension and Depth Dependent Upper Bounds in Polynomial Ideal Theory

Co-author(s): Amir Hashemi

Reference: Journal of Symbolic Computation, accepted for publication (2019)

Description: We improve certain degree bounds for Gröbner 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 Gröbner basis (w.r.t. the degree reverse lexicographical ordering) of a homogeneous ideal in these positions.

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