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Fano $4$-folds with nef tangent bundle in positive characteristic (2210.17055v1)

Published 31 Oct 2022 in math.AG, math.CV, and math.DG

Abstract: In characteristic $0$, the Campana-Peternell conjecture claims that the only smooth Fano variety with nef tangent bundle should be homogeneous. In this paper, we study the positive characteristic version of the Campana-Peternell conjecture. In particular, we give an affirmative answer for Fano $4$-folds with nef tangent bundle and Picard number greater than one.

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