Quasi-Gorenstein extended Rees algebras associated with filtrations

TL;DR

This paper characterizes when extended Rees algebras associated with Hilbert filtrations are quasi-Gorenstein, linking this property to Cohen-Macaulayness of local cohomology modules and providing necessary and sufficient conditions.

Contribution

It offers new criteria for the quasi-Gorenstein property of extended Rees algebras based on local cohomology and Cohen-Macaulay conditions, advancing understanding in algebraic geometry.

Findings

Necessary and sufficient conditions for quasi-Gorenstein property

Characterization in terms of local cohomology length

Deformation criteria for the property

Abstract

This paper investigates the quasi-Gorenstein property of extended Rees algebras associated with the Hilbert filtrations on a Noetherian local ring. We provide necessary and sufficient conditions for the deformation of the quasi-Gorenstein property, characterized by the Cohen-Macaulayness of the Matlis dual of local cohomology modules. As a consequence, we offer a characterization of the quasi-Gorenstein property of extended Rees algebras in terms of conditions on the length of local cohomology.