Recombination formulae for the spectrum of curve singularities and some applications

2014/03/23 by Dmitry Kerner, Kerner, Dmitry
Mathematics · Computer Science · #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1403.5789

Abstract

We obtain some recombination formulae for the spectra of (complex, reduced) plane curve singularities. As an application we prove: a generalization of Durfee's bound; a generalization of Givental's bound; the multiplicity of the curve singularity is determined by its spectrum; for many curve singularities all the multiplicities of exceptional divisors of the resolution are determined by the spectrum; etc.

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