We present an effective method to compute the resolution regularity (vector) of bihomogeneous ideals. For this purpose, we first introduce the new notion of an xPommaret basis and describe an algorithm to compute a linear change of coordinates for a given bihomogeneous ideal such that the new ideal obtained after performing this change possesses a finite xPommaret basis. Then, we show that the xcomponent of the bigraded regularity of a bihomogeneous ideal is equal to the xdegree of its xPommaret basis (after performing the mentioned linear change of variables). Finally, we introduce the new notion of an ideal in xquasi stable position and show that a bihomogeneous ideal has a finite xPommaret basis iff it is in xquasi stable position.
Download TeX format
