Ultra-test ideals in rings with finitely generated anti-canonical algebras

TL;DR

This paper introduces ultra-test ideals in rings with finitely generated anti-canonical algebras, providing a new characterization via ultra-Frobenii and offering an alternative proof of a key result relating klt type rings and their pure subrings.

Contribution

It develops a novel characterization of adjoint ideals using ultra-Frobenii in the context of finitely generated anti-canonical rings, extending the understanding of klt type rings.

Findings

Characterization of adjoint ideals via ultra-Frobenii.

Alternative proof of the preservation of klt type under pure subrings.

Enhanced understanding of anti-canonical rings with finitely generated structures.

Abstract

When anti-canonical rings are finitely generated, we give a characterization of adjoint ideals using ultra-Frobenii, a characteristic zero analogue of Frobenius morphisms. This characterization enables us to give an alternative proof of a result of Zhuang, which states that if a ring is of klt type, then so is any of its pure subrings.