English

Smooth 3-dimensional canonical thresholds

Algebraic Geometry 2016-03-15 v3

Abstract

If XX is an algebraic variety with at worst canonical singularities and SS is a \Q\Q-Cartier hypersurface in XX, the canonical threshold of the pair (X,S)(X,S) is the supremum of cRc\in\R such that the pair (X,cS)(X,cS) is canonical. We show that the set of all possible canonical thresholds of the pairs (X,S)(X,S), where XX is a germ of smooth 3-dimensional variety, satisfies the ascending chain condition. We also deduce a formula for the canonical threshold of (\C3,S)(\C^3,S), where S is a Brieskorn singularity.

Cite

@article{arxiv.0912.3186,
  title  = {Smooth 3-dimensional canonical thresholds},
  author = {D. A. Stepanov},
  journal= {arXiv preprint arXiv:0912.3186},
  year   = {2016}
}

Comments

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

R2 v1 2026-06-21T14:24:41.951Z