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arXiv · 2409.14251

The log canonical threshold of products of ideals and mixed \L ojasiewicz exponents

Carles Bivià-Ausina
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Abstract

Given two ideals $I$ and $J$ of the ring $\mathcal O_n$ of analytic function germs $f:(\mathbb C^n,0)\to \mathbb C$, we show a sharp lower bound for the log canonical threshold of $IJ$ in terms of the sequences of mixed {\L}ojasiewicz exponents of them. In particular, in the case where $J$ is the maximal ideal, the corresponding equality holds if and only if the integral closure of $I$ equals some power of the maximal ideal.

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Carles Bivià-Ausina. 2024-09-21. The log canonical threshold of products of ideals and mixed \L ojasiewicz exponents. https://arxiv.org/abs/2409.14251

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