We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in (resp. ). 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 . 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 (resp. ). 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 . Cela donne une nouvelle preuve d’un théorème de Phong-Sturm.
Keywords: Resolution of singularities, log-canonical threshold, ascending chain condition
Mot clés : Résolution des singularités, seuil log-canonique, condition de chaîne ascendante
@article{AIF_2018__68_7_2883_0, author = {Collins, Tristan C.}, title = {Log-canonical thresholds in real and complex dimension~2}, journal = {Annales de l'Institut Fourier}, pages = {2883--2900}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {68}, number = {7}, year = {2018}, doi = {10.5802/aif.3229}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.3229/} }
TY - JOUR AU - Collins, Tristan C. TI - Log-canonical thresholds in real and complex dimension 2 JO - Annales de l'Institut Fourier PY - 2018 SP - 2883 EP - 2900 VL - 68 IS - 7 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3229/ DO - 10.5802/aif.3229 LA - en ID - AIF_2018__68_7_2883_0 ER -
%0 Journal Article %A Collins, Tristan C. %T Log-canonical thresholds in real and complex dimension 2 %J Annales de l'Institut Fourier %D 2018 %P 2883-2900 %V 68 %N 7 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3229/ %R 10.5802/aif.3229 %G en %F AIF_2018__68_7_2883_0
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. http://archive.numdam.org/articles/10.5802/aif.3229/
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