For t in N, E.Miller has defined a category of positively t-determined modules over the polynomial ring S in n variables. We consider the AuslanderReiten translate, Nt, on the (derived) category of such modules. A monomial ideal I is t-determined if each generator x has a ≤ t. We compute the multigraded cohomology and betti spaces of N k t (S/I) for every iterate k and also the S-module structu...

The Euler–Koszul complex is the fundamental tool in the homological study of A-hypergeometric differential systems and functions. We compare Euler–Koszul homology with D-module direct images from the torus to the base space through orbits in the corresponding toric variety. Our approach generalizes a result by Gel’fand et al. [GKZ90, Thm. 4.6] and yields a simpler, more algebraic proof. In the ...

The notion of epsilon multiplicity was originally defined by Ulrich and Validashti as a limsup, they used it to detect integral dependence modules. It is important know if can be realized limit. In this article, we show that the relative reduced Noetherian graded algebras over an excellent local ring exists An special case Cutkosky’s result concerning obtained corollary our main theorem. We als...