Seven combinatorial problems around isolated quasihomogeneous singularities


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.

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Correspondence to Claus Hertling.

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This work was supported by the DFG Grant He2287/4-1 (SISYPH).

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Hertling, C., Zilke, P. Seven combinatorial problems around isolated quasihomogeneous singularities. J Algebr Comb 50, 447–482 (2019).

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

Mathematics Subject Classification

  • 32S40
  • 12Y05
  • 05C22
  • 05C25