ACC for minimal log discrepancies of exceptional singularities

TL;DR

This paper establishes the existence of complements and the ACC for minimal log discrepancies in exceptional singularities, advancing the understanding of singularity theory in algebraic geometry.

Contribution

It introduces the theory of complements for real coefficients and proves the ACC for minimal log discrepancies of exceptional singularities.

Findings

Proves the existence of $n$-complements for pairs with DCC coefficients.

Establishes the ACC for minimal log discrepancies of exceptional singularities.

Develops the theory of complements for real coefficients.

Abstract

We prove the existence of $n$-complements for pairs with DCC coefficients and the ACC for minimal log discrepancies of exceptional singularities. In order to prove these results, we develop the theory of complements for real coefficients. We introduce $(n,\Gamma_0)$-decomposable $\mathbb{R}$-complements, and show its existence for pairs with DCC coefficients.