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arXiv · 2204.02045

On the Iitaka conjecture for anticanonical divisors in positive characteristic

Marta Benozzo
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Abstract

Given a fibration over a perfect field of positive characteristic, we study an Iitaka-type inequality for the anticanonical divisors. We conclude that it holds when the source of the fibration is a threefold or when the target is a curve, the general fibre is regular and the pair induced on it from the ambient space is strongly F-regular. We then give counterexamples in characteristics 2 and 3 for fibrations with non-normal fibres, constructed from Tango--Raynaud surfaces.

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Marta Benozzo. 2022-04-05. On the Iitaka conjecture for anticanonical divisors in positive characteristic. https://doi.org/10.1307/mmj/20226272

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