Smooth 3-dimensional canonical thresholds

Abstract

If $X$ is an algebraic variety with at worst canonical singularities and $S$ is a $\Q$-Cartier hypersurface in $X$, the canonical threshold of the pair $(X,S)$ is the supremum of $c\in \mathbb{R}$ such that the pair $(X,cS)$ is canonical. We show that the set of all possible canonical thresholds of the pairs $(X,S)$, where $X$ is a germ of smooth 3-dimensional variety, satisfies the ascending chain condition. We also deduce a formula for the canonical threshold of $(\C^3,S)$, where S is a Brieskorn singularity.

Dedicated to the memory of my advisor Vasilii Alekseevich Iskovskikh. 14 pages; v3: minor corrections

References in corpus (3)

• Shokurov's ACC Conjecture for log canonical thresholds on smooth varieties
• Which powers of holomorphic functions are integrable?
• Limits of log canonical thresholds