Log-canonical thresholds in real and complex dimension 2

2017/07/27 by Collins, Tristan C.
#Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.08994

Abstract

We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in ℂ² (resp. ℝ²). 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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