Vanishing theorems for Fano threefolds in positive characteristic

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Abstract

We prove that Kodaira vanishing holds for an arbitrary smooth Fano threefold in positive characteristic. To this end, we show that it is quasi-F-split when the Picard number or the Fano index is larger than one. We also establish Akizuki-Nakano vanishing for smooth Fano threefolds when the Picard number or the Fano index is larger than one, and therefore they lift to the ring of Witt vectors.

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Kawakami et al. (Sat,) studied this question.

synapsesocial.com/papers/68e7031db6db64358767cea8 https://doi.org/https://doi.org/10.48550/arxiv.2404.04764

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