Log-canonical thresholds in real and complex dimension 2
Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2883-2900.

We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in 2 (resp. 2 ). In particular, we prove that the ascending chain condition holds, and that the positive accumulation points of decreasing sequences are precisely the integrability indices of holomorphic (resp. real analytic) functions in dimension 1. This gives a new proof of a theorem of Phong–Sturm.

Nous étudions l’ensemble des seuils log-canoniques (ou indices d’intégrabilité critiques) des germes de fonctions holomorphes (resp. réel analytiques) dans 2 (resp. 2 ). En particulier, nous prouvons que la condition de la chaîne ascendante est vraie et que les points d’accumulation positifs des séquences décroissantes sont précisément les indices d’intégrabilité des fonctions holomorphes (resp. réel analytiques) en dimension 1. Cela donne une nouvelle preuve d’un théorème de Phong-Sturm.

Published online:
DOI: 10.5802/aif.3229
Classification: 14E15,  32S45
Keywords: Resolution of singularities, log-canonical threshold, ascending chain condition
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Collins, Tristan C. Log-canonical thresholds in real and complex dimension 2. Annales de l'Institut Fourier, Volume 68 (2018) no. 7, pp. 2883-2900. doi : 10.5802/aif.3229. https://aif.centre-mersenne.org/articles/10.5802/aif.3229/

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