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arXiv · 2506.13603

On volumes and the generic invariance of Fano type varieties

Donghyeon Kim
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Abstract

We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$.

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Donghyeon Kim. 2026-06-16. On volumes and the generic invariance of Fano type varieties. https://arxiv.org/abs/2506.13603

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