April 25, 2024Open Access

Boundedness of log Fano cone singularities and discreteness of local volumes

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Abstract

We prove that in any fixed dimension, K-semistable log Fano cone singularities whose volumes are bounded from below by a fixed positive number form a bounded set. As a consequence, we show that the set of local volumes of klt singularities of a fixed dimension has zero as the only accumulation point.

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Xu et al. (Thu,) studied this question.

synapsesocial.com/papers/68e6d998b6db643587656899 https://doi.org/https://doi.org/10.48550/arxiv.2404.17134

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3Boundedness of Log Fano Pairs with Certain K-stability2024 · 1 citations
4On existence of bounded relative-global complements for Fano fibrations2024
5Exceptional Fano varieties with small minimal log discrepancy2026

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