Abstract
We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in ℂ 2 (resp. ℝ 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.
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