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arXiv · 1707.08994

Log-canonical thresholds in real and complex dimension 2

Tristan C. Collins
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Abstract

We study the set of log-canonical thresholds (or critical integrability indices) of holomorphic (resp. real analytic) function germs in $\mathbb{C}^2$ (resp. $\mathbb{R}^2$). 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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Tristan C. Collins. 2017-07-27. Log-canonical thresholds in real and complex dimension 2. https://arxiv.org/abs/1707.08994

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