Towards finite generation of the canonical ring without the MMP

TL;DR

This paper initiates a project to prove the finite generation of the log canonical ring without relying on Mori theory, aiming to advance algebraic geometry methods.

Contribution

It introduces a novel approach to establish finite generation of the log canonical ring independent of the Minimal Model Program.

Findings

First step towards MMP-free proof of finite generation

New techniques for log canonical ring analysis

Foundation for subsequent proof development

Abstract

This paper is the first of two steps in a project to prove finite generation of the log canonical ring without Mori theory.