Canonical Modules and Class Groups of Rees-Like Algebras

Abstract

Rees-like algebras have played a major role in settling the Eisenbud–Goto conjecture. This paper concerns the structure of the canonical module of the Rees-like algebra and its class groups. Via an explicit computation based on linkage, we provide an explicit and surprisingly well-structured resolution of the canonical module in terms of a type of double-Koszul complex. Additionally, we give descriptions of both the divisor class group and the Picard group of a Rees-like algebra.