ACC for minimal log discrepancies of exceptional singularities

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 $(n,\hat{I}{“}_0)$-decomposable $\mathbb{R}$-complements, and show its existence for pairs with DCC coefficients.

74 pages, proof in section 6 is simplified, section 8 is new. Submitted version, comments are very welcome!