Spectrum and Hertling Conjecture for Trimodal Singularities

The spectrum is an important numerical invariant of an isolated hypersurface singularity, linking its topological and analytic structures. The well-known Hertling conjecture describes the relation between the range and variance of the exponents, i.e., elements of the spectrum. We compute the spectra of trimodal singularities and verify the Hertling conjecture for them.