On exceptional quotient singularities

Abstract

We study exceptional quotient singularities. In particular, we prove an exceptionality criterion in terms of the $\alpha$-invariant of Tian, and utilize it to classify four-dimensional and five-dimensional exceptional quotient singularities.

30 pages, improved exposition, shifted numeration

References in corpus (3)

• Some discretizations of geometric evolution equations and the Ricci iteration on the space of Kahler metrics, I
• Blow-ups of canonical singularities
• On purely log terminal blow-ups

Cited by in corpus (15)

• Boundedness of $\mathbb{Q}$-Fano varieties with degrees and alpha-invariants bounded from below
• ACC for minimal log discrepancies of exceptional singularities
• Basis log canonical thresholds, local intersection estimates, and asymptotically log del Pezzo surfaces
• Super-rigid Affine Fano Varieties
• Nine-dimensional exceptional quotient singularities exist
• On the sharpness of Tian's criterion for K-stability
• Convergence of the Kähler-Ricci iteration
• Five-Dimensional Weakly Exceptional Quotient Singularities
• Jordan constant for Cremona group of rank 3
• Sporadic simple groups and quotient singularities
• Three embeddings of the Klein simple group into the Cremona group of rank three
• G-coregularity of del Pezzo surfaces
• On K-stability of Fano weighted hypersurfaces
• Weakly-exceptional singularities in higher dimensions
• Weakly-exceptional quotient singularities in prime dimension