Alpha-invariants and purely log terminal blow-ups

TL;DR

This paper establishes a new inequality involving alpha-invariants of Kollár components in Kawamata log terminal singularities, contributing to the understanding of singularity invariants in algebraic geometry.

Contribution

It proves that the sum of alpha-invariants of two different Kollár components of a Kawamata log terminal singularity is less than 1, a novel inequality in the field.

Findings

Sum of alpha-invariants of two Kollár components is less than 1

Provides new bounds for invariants of singularities

Advances understanding of singularity classification

Abstract

We prove that the sum of the $\alpha$-invariants of two different Koll\'ar components of a Kawamata log terminal singularity is less than $1$.