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arXiv · 2404.17134

Boundedness of log Fano cone singularities and discreteness of local volumes

Chenyang Xu·Ziquan Zhuang
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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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Chenyang Xu, Ziquan Zhuang. 2024-04-26. Boundedness of log Fano cone singularities and discreteness of local volumes. https://arxiv.org/abs/2404.17134

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