Dualizing complexes of seminormal affine semigroup rings and toric face rings

TL;DR

This paper characterizes seminormality and normality of affine semigroup rings and toric face rings using dualizing complexes and canonical modules, providing new insights into their algebraic structure.

Contribution

It introduces characterizations of seminormality and normality for these rings based on dualizing complexes and canonical modules, extending previous understanding.

Findings

Seminormality of affine semigroup rings characterized via dualizing complexes.

Normality of Cohen-Macaulay semigroup rings linked to the shape of the canonical module.

Seminormality of toric face rings characterized through dualizing complexes.

Abstract

We characterize the seminormality of an affine semigroup ring in terms of the dualizing complex, and the normality of a Cohen-Macaulay semigroup ring by the "shape" of the canonical module. We also characterize the seminormality of a toric face ring in terms of the dualizing complex. A toric face ring is a simultaneous generalization of Stanley-Reisner rings and affine semigroups.