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.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
