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Mat. Zametki, 2011, Volume 90, Issue 2, Pages 285–299 (Mi mz8713)  

This article is cited in 1 scientific paper (total in 1 paper)

Smooth Three-Dimensional Canonical Thresholds

D. A. Stepanov

N. E. Bauman Moscow State Technical University

Abstract: 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, $\mathbb{Q}$-Cartier hypersurface, Brieskorn singularity, minimal model program, Picard number

DOI: https://doi.org/10.4213/mzm8713

Full text: PDF file (583 kB)
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English version:
Mathematical Notes, 2011, 90:2, 265–278

Bibliographic databases:

UDC: 512.72
Received: 18.01.2010
Revised: 08.07.2010

Citation: D. A. Stepanov, “Smooth Three-Dimensional Canonical Thresholds”, Mat. Zametki, 90:2 (2011), 285–299; Math. Notes, 90:2 (2011), 265–278

Citation in format AMSBIB
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\by D.~A.~Stepanov
\paper Smooth Three-Dimensional Canonical Thresholds
\jour Mat. Zametki
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\issue 2
\pages 285--299
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\crossref{https://doi.org/10.4213/mzm8713}
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\transl
\jour Math. Notes
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\vol 90
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\pages 265--278
\crossref{https://doi.org/10.1134/S0001434611070261}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
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