On subadditivity of Kodaira dimension in positive characteristic

Abstract

We show that for a surjective, separable morphism f of smooth projective varieties over an algebraically closed field of positive characteristic such that $f_{\ast }{\mathcal{O}}_X={\mathcal{O}}_Y$ subadditivity of Kodaira dimension holds, provided the base is of general type and the Hasse-Witt matrix of the geometric general fiber is not nilpotent.

24 pages, comments are welcomed

References in corpus (2)

• Depth of $F$-singularities and base change of relative canonical sheaves
• On the three dimensional minimal model program in positive characteristic

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• Abundance for non-uniruled 3-folds with non-trivial Albanese maps in positive characteristics
• Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics
• Iitaka's $C_{n,m}$ conjecture for 3-folds in positive characteristic
• A note on Iitaka's conjecture $C_{3,1}$ in positive characteristics
• Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers