Geodesic
Smooth Three-Dimensional Canonical Thresholds
Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 285-299

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If $X$ is an algebraic variety with at most canonical singularities and $S$ is a $\mathbb{Q}$-Cartier hypersurface in $X$, then the canonical threshold of the pair $(X,S)$ is defined as the least upper bound of the reals $c$ for which the pair $(X,cS)$ is canonical. We show that the set of all possible canonical thresholds of the pairs $(X,S)$, where $X$ is smooth and three-dimensional, satisfies the ascending chain condition. We also derive a formula for the canonical threshold of the pair $(\mathbb{C}^3,S)$, where $S$ is a Brieskorn singularity.
Keywords: algebraic variety, canonical singularity, canonical threshold, Brieskorn singularity, minimal model program, Picard number.
Mots-clés : $\mathbb{Q}$-Cartier hypersurface 
@article{MZM_2011_90_2_a10,
     author = {D. A. Stepanov},
     title = {Smooth {Three-Dimensional} {Canonical} {Thresholds}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {285--299},
     publisher = {mathdoc},
     volume = {90},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a10/}
}
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D. A. Stepanov. Smooth Three-Dimensional Canonical Thresholds. Matematičeskie zametki, Tome 90 (2011) no. 2, pp. 285-299. http://geodesic.mathdoc.fr/item/MZM_2011_90_2_a10/