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IPM
30
YEARS OLD

“School of Mathematics”

Paper   IPM / M / 15946
   School of Mathematics
  Title: Computing the resolution regularity of bi-homogeneous ideals
  Author(s): Amir Hashemi (Joint with N. Aramideh and W. M. Seiler)
  Status: Published
  Journal: J. Symb. Comput.
  Year: 2020
  Pages: Doi: 10.1016/j.jsc.2019.12.001
  Supported by: IPM
  Abstract:
We present an effective method to compute the resolution regularity (vector) of bi-homogeneous ideals. For this purpose, we first introduce the new notion of an x-Pommaret basis and describe an algorithm to compute a linear change of coordinates for a given bi-homogeneous ideal such that the new ideal obtained after performing this change possesses a finite x-Pommaret basis. Then, we show that the x-component of the bi-graded regularity of a bi-homogeneous ideal is equal to the x-degree of its x-Pommaret basis (after performing the mentioned linear change of variables). Finally, we introduce the new notion of an ideal in x-quasi stable position and show that a bi-homogeneous ideal has a finite x-Pommaret basis iff it is in x-quasi stable position.

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