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arXiv · 2401.06074

On the Albanese morphism of varieties with Frobenius stable Kodaira dimension zero

Jefferson Baudin
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Abstract

We show that in positive characteristic, the Albanese morphism of normal proper varieties $X$ with $\kappa_S(X, \omega_X) = 0$ is separable, surjective, has connected fibers, and the generic fiber $F$ also satisfies $\kappa(F, \omega_F) = 0$. As a corollary, we deduce a new case of Iitaka's subadditivity conjecture for fibrations over abelian varieties, when the generic fiber has non-nilpotent Hasse-Witt matrix.

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Jefferson Baudin. 2024-01-11. On the Albanese morphism of varieties with Frobenius stable Kodaira dimension zero. https://arxiv.org/abs/2401.06074

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