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

arXiv comment74 pages, proof in section 6 is simplified, section 8 is new. Submitted version, comments are very welcome!

References in corpus (10)

• Finiteness of algebraic fundamental groups
• Blow-ups of canonical singularities
• On exceptional quotient singularities
• Birational boundedness of rationally connected Calabi-Yau 3-folds
• On minimal log discrepancies on varieties with fixed Gorenstein index
• Toward the equivalence of the ACC for $a$-log canonical thresholds and the ACC for minimal log discrepancies
• Existence and boundedness of $n$-complements
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three
• ACC for log canonical threshold polytopes
• Non-vanishing theorem for lc pairs admitting a Calabi--Yau pair

Cited by in corpus (22)

• Birational boundedness of rationally connected Calabi-Yau 3-folds
• The Jordan property for local fundamental groups
• Toward the equivalence of the ACC for $a$-log canonical thresholds and the ACC for minimal log discrepancies
• Existence and boundedness of $n$-complements
• A gap theorem for minimal log discrepancies of non-canonical singularities in dimension three
• Shokurov's conjecture on conic bundles with canonical singularities
• Inversion of adjunction for quotient singularities
• Existence of flips for generalized lc pairs
• Log canonical $3$-fold complements
• Boundedness of $(\epsilon ,n)$-Complements for Surfaces
• Kawamata log terminal singularities of full rank
• An optimal gap of minimal log discrepancies of threefold non-canonical singularities
• Complements and coregularity of Fano varieties
• On the sharpness of Tian's criterion for K-stability
• Boundedness of ($\epsilon ,n$)-Complements for projective generalized pairs of Fano type
• Effective birationality for sub-pairs with real coefficients
• On singularities of threefold weighted blowups
• Number of singular points on projective surfaces
• A variant of the effective adjunction conjecture with applications
• On termination of flips and fundamental groups
• Rational nef and anti-nef polytopes are not uniform
• Bounded Complements for Weak Fano Pairs with Alpha-invariants and Volumes Bounded Below