Global Frobenius Liftability II: Surfaces and Fano Threefolds

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.

24 pages. Comments welcome! This is the second part of the paper arXiv:1708.03777 which was split off the original article "Liftability of the Frobenius morphism and images of toric varieties" in the review process and then revised