[Problème de Nash pour une paire torique et la log-discrépance minimale]
Dans cette Note, nous formulons le problème de Nash pour une paire constituée d'une variété torique et d'un idéal invariant. Nous montrons que le problème admet une réponse positive. Nous montrons aussi que la log-discrépance minimale, si elle est finie, est calculée par un diviseur correspondant à une composante de Nash. D'autre part, si la log-discrépance minimale est −∞, alors il existe une composante de Nash dont le diviseur correspondant est de log-discrépance négative.
This Note formulates the Nash problem for a pair consisting of a toric variety and an invariant ideal and gives an affirmative answer to the problem. We also prove that the minimal log-discrepancy is computed by a divisor corresponding to a Nash component, if the minimal log-discrepancy is finite. On the other hand there exists a Nash component such that the corresponding divisor has negative log-discrepancy, if the minimal log-discrepancy is −∞.
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@article{CRMATH_2010__348_17-18_985_0,
author = {Ishii, Shihoko},
title = {The {Nash} problem for a toric pair and the minimal log-discrepancy},
journal = {Comptes Rendus. Math\'ematique},
pages = {985--988},
publisher = {Elsevier},
volume = {348},
number = {17-18},
year = {2010},
doi = {10.1016/j.crma.2010.07.034},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.07.034/}
}
TY - JOUR AU - Ishii, Shihoko TI - The Nash problem for a toric pair and the minimal log-discrepancy JO - Comptes Rendus. Mathématique PY - 2010 SP - 985 EP - 988 VL - 348 IS - 17-18 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.07.034/ DO - 10.1016/j.crma.2010.07.034 LA - en ID - CRMATH_2010__348_17-18_985_0 ER -
%0 Journal Article %A Ishii, Shihoko %T The Nash problem for a toric pair and the minimal log-discrepancy %J Comptes Rendus. Mathématique %D 2010 %P 985-988 %V 348 %N 17-18 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.07.034/ %R 10.1016/j.crma.2010.07.034 %G en %F CRMATH_2010__348_17-18_985_0
Ishii, Shihoko. The Nash problem for a toric pair and the minimal log-discrepancy. Comptes Rendus. Mathématique, Tome 348 (2010) no. 17-18, pp. 985-988. doi : 10.1016/j.crma.2010.07.034. http://www.numdam.org/articles/10.1016/j.crma.2010.07.034/
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