Toward finite generation of higher rational rank valuations

TL;DR

This paper introduces a conjecture on finite generation related to valuations that determine the stability of log Fano pairs and proposes a degeneration approach to address it.

Contribution

It formulates a new finite generation conjecture for valuations in the context of log Fano pairs and initiates a degeneration strategy to prove it.

Findings

Conjecture on finite generation of certain valuations.

Degeneration strategy proposed for attacking the conjecture.

Foundation laid for future proof of the conjecture.

Abstract

We propose a finite generation conjecture for the valuation which computes the stability threshold of a log Fano pair. We also initiate a degeneration strategy of attacking the conjecture.