Computing the resolution regularity of bi-homogeneous ideals. (March 2021) - Aramideh, Nasibeh; Hashemi, Amir; Seiler, Werner M.
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.