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Seven combinatorial problems around isolated quasihomogeneous singularities

  • Claus Hertling
  • Philip Zilke
Article
  • 11 Downloads

Abstract

This paper proposes seven combinatorial problems around formulas for the characteristic polynomial and the spectral numbers of an isolated quasihomogeneous hypersurface singularity. One of them is a new conjecture on the characteristic polynomial. It is an amendment to an old conjecture of Orlik on the integral monodromy of an isolated quasihomogeneous singularity. The search for a combinatorial proof of the new conjecture led us to the seven purely combinatorial problems.

Keywords

Isolated quasihomogeneous singularity Weight system Monodromy Characteristic polynomial Combinatorial problems Orlik blocks 

Mathematics Subject Classification

32S40 12Y05 05C22 05C25 

Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Lehrstuhl für Mathematik VIUniversität MannheimMannheimGermany

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