Spectrum and Hertling Conjecture for Trimodal Singularities

Quan Shi, Yang Wang, Huaiqing Zuo

Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

Abstract: 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.

Keywords: isolated singularity, spectrum, Newton non-degenerate singularity, Hertling conjecture.

Received: June 3, 2024
Revised: September 5, 2024
Accepted: September 26, 2024

DOI: 10.4213/tm4448

 English version: Proceedings of the Steklov Institute of Mathematics, 2025, 330, 375–393

Bibliographic databases:

•