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Global Frobenius Liftability II: Surfaces and Fano Threefolds

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arxiv 2102.02788 v1 pith:WOR56MAK submitted 2021-02-04 math.AG

Piotr Achinger , Jakub Witaszek , Maciej Zdanowicz This is my paper · ORCID
classification math.AG
keywords frobeniusliftingsfanogloballiftabilitysurfacesthreefoldsunder
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abstract

In this article, a sequel to "Global Frobenius Liftability I" (math:1708:03777v2), we continue the development of a comprehensive theory of Frobenius liftings modulo $p^2$. We study compatibility of divisors and closed subschemes with Frobenius liftings, Frobenius liftings of blow-ups, descent under quotients by some group actions, stability under base change, and the properties of associated F-splittings. Consequently, we characterise Frobenius liftable surfaces and Fano threefolds, confirming the conjecture stated in our previous paper.

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  1. Images of toric variety and amplified endomorphism of weak Fano threefolds

    math.AG 2025-06 conditional novelty 5.0 of 10

    A smooth projective weak Fano threefold of Picard rank 2 that is either a toric image or admits an int-amplified endomorphism is toric, with three explicit non-Fano exceptions.

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