Missing spectral numbers between Steenbrink and Tjurina spectra for hypersurface singularities exhibit canonical graded symmetry from Jacobian ring self-duality.
Exponents of an irreducible plane curve singularity
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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.
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Tjurina spectrum and graded symmetry of missing spectral numbers
Missing spectral numbers between Steenbrink and Tjurina spectra for hypersurface singularities exhibit canonical graded symmetry from Jacobian ring self-duality.