Limit spectral distribution for non-degenerate hypersurface singularities

Patricio Almirón; Mathias Schulze

doi:10.5802/crmath.335

Algèbre, Analyse et géométrie complexes

Limit spectral distribution for non-degenerate hypersurface singularities

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

Comptes Rendus. Mathématique, Volume 360 (2022), pp. 699-710.

Résumé

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.

Reçu le : 2021-07-21
Révisé le : 2022-01-22
Accepté le : 2022-01-22
Publié le : 2022-06-22

Zbl

DOI : 10.5802/crmath.335

Classification : 32S25, 32S35, 42A38

Affiliations des auteurs :

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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     title = {Limit spectral distribution for non-degenerate hypersurface singularities},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {699--710},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {360},
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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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