Sliding Functor and Polarization Functor for Multigraded Modules

Abstract

We define sliding functors, which are exact endofunctors of the category of multigraded modules over a polynomial ring. They preserve several invariants of modules, especially the (usual) depth and Stanley depth. In a similar way, we can also define the polarization functor. While this idea has appeared in papers of Bruns–Herzog and Sbarra, we give slightly different approach. Keeping these functors in mind, we treat simplicial spheres of Bier–Murai type.