Comptes Rendus
Algèbre, Analyse et géométrie complexes
Limit spectral distribution for non-degenerate hypersurface singularities
Patricio Almirón1  ; Mathias Schulze2
1 Instituto de Matemática Interdisciplinar (IMI), Departamento de Álgebra, Geometría y Topología Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain
2 Department of Mathematics, TU Kaiserslautern, 67663 Kaiserslautern, Germany
Comptes Rendus. Mathématique, Volume 360 (2022), pp. 699-710.

We establish Kyoji Saito’s continuous limit distribution for the spectrum of Newton non-degenerate hypersurface singularities. Investigating Saito’s notion of dominant value in the case of irreducible plane curve singularities, we find that the log canonical threshold is strictly bounded below by the doubled inverse of the Milnor number. We show that this bound is asymptotically sharp.

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DOI : 10.5802/crmath.335
Classification : 32S25, 32S35, 42A38
Patricio Almirón 1 ; Mathias Schulze 2

1 Instituto de Matemática Interdisciplinar (IMI), Departamento de Álgebra, Geometría y Topología Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040, Madrid, Spain
2 Department of Mathematics, TU Kaiserslautern, 67663 Kaiserslautern, Germany
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Patricio Almirón; Mathias Schulze. Limit spectral distribution for non-degenerate hypersurface singularities. Comptes Rendus. Mathématique, Volume 360 (2022), pp. 699-710. doi : 10.5802/crmath.335. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.335/

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