Shift modules, strongly stable ideals, and their dualities

Abstract

We enrich the setting of strongly stable ideals (SSI): We introduce shift modules, a module category encompassing SSIs. The recently introduced duality on SSIs is given an effective conceptual and computational setting. We study SSIs in infinite dimensional polynomial rings, where the duality is most natural. Finally a new type of resolution for SSIs is introduced. This is the projective resolution in the category of shift modules.