On Shokurov-type b-divisorial algebras of higher rank

TL;DR

This paper develops foundational techniques for higher rank b-divisorial algebras of Shokurov type, proposes conjectures, and confirms them in the case of affine curves, advancing the understanding of these algebraic structures.

Contribution

It introduces new methods for studying higher rank b-divisorial algebras and formulates conjectures, providing partial confirmation in the case of affine curves.

Findings

Conjectures on Shokurov and adjoint algebras are confirmed for affine curves.

Developed techniques for higher rank b-divisorial algebra analysis.

Established foundational results for future research in algebraic geometry.

Abstract

The purpose of this paper is to lay the foundations for the theory of higher rank b-divisorial algebras of Shokurov type. We develop techniques to deal with such objects and propose two natural conjectures regarding Shokurov algebras and adjoint algebras. We confirm these conjectures in the case of affine curves.