Exponents of an irreducible plane curve singularity

2000/09/13 by Morihiko Saito, Saito, Morihiko · 1 citation
Computer Science · Mathematics · #32S35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:32S35

paper · pdf · doi:10.48550/arxiv.math/0009133

AMS-TeX, 15 pages; remarks and references added

openalex publication_date 2000/09/13 · arxiv created 2000/09/26 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give an explicit formula for the exponents (i.e. the spectra up to the shift by one) of an irreducible plane curve singularity in terms of Puiseux pairs. As an application we prove in this case Hertling's conjecture that the variance (i.e. the square of the standard deviation) of the exponents is bounded by the difference between the maximal and minimal exponents divided by 12.

Citations

• Variance of the spectral numbers

Cited by

• Bernstein polynomial and value set of differentials for plane branches

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