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Which powers of holomorphic functions are integrable?

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arxiv 0805.0756 v1 pith:IDFBBX4K submitted 2008-05-06 math.AG math.CV

classification math.AGmath.CV
keywords canonicalfunctionseveryfunctionholomorphicintegrablelimitn-variable
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We show that every limit of log canonical thresholds of n-variable functions is also a log canonical threshold of an (n-1)-variable function.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Minimal log discrepancies on a fixed threefold

    math.AG 2024-12 conditional novelty 7.0 of 10

    ACC for minimal log discrepancies is proved for every fixed normal threefold.

  2. Bounds on the F-Pure Threshold of Isolated Hypersurface Singularities

    math.AG 2026-05 unverdicted novelty 6.0 of 10

    Derives bounds on F-pure threshold of isolated hypersurface singularities in terms of Milnor/Tjurina numbers and value semigroups, yielding positive-char analogue of Igusa's formula with applications to log canonical ...

  3. A lower bound on the analytic log-canonical threshold over local fields of positive characteristic

    math.AG 2025-11 conditional novelty 6.0 of 10

    For local fields of positive characteristic, every nonzero analytic function has strictly positive integrability threshold, and for regular functions on smooth varieties the threshold is at least 1/(d·D^m).

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