Trace ideals of canonical modules over Schubert cycles and determinantal rings

TL;DR

This paper investigates the structure of canonical trace ideals in Schubert cycles and determinantal rings, providing explicit descriptions of singular loci and analyzing the stability of the CTR property.

Contribution

It offers a detailed description of the non-Gorenstein locus and characterizes the CTR property for determinantal rings, advancing understanding of their singularities.

Findings

Explicit description of the non-Gorenstein locus

Stability of the CTR property under base change

Characterization of the CTR property in determinantal rings

Abstract

In this paper, we study the canonical trace of Schubert cycles and determinantal rings. As an application, we give an explicit description of the non-Gorenstein locus and show that its structure is compatible with the known representations of the singular locus and the canonical module. Furthermore, for the CTR property recently introduced by Miyazaki, we establish its stability under base change and provide a characterization in the case of determinantal rings.