Computing the Resolution Regularity of Bi-Homogeneous Ideals
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Co-author(s): Nasibeh Aramideh and Amir Hashemi |
Reference: Journal of Symbolic Computation, 103 (2021) 141-156 |
Description: An important result about Pommaret bases asserts that their degree is just
the Castelnuovo-Mumford regularity of the ideal generated by them. In this
paper, we are concerned with an extension of this result to bi-homogeneous
ideals. Here the resolution regularity is defined as a two-dimensional
vector. We introduce the new concept of an x-Pommaret basis and show how
it allows us to determine one component of this vector (this other one can
be determined by swapping the role of the variables). As a by-product, we
define the notion of an x-quasi-stable monomial ideal and show that an
ideal possesses an x-Pommaret basis, if and only if its leading ideal is
x-quasi-stable. |
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