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# Mathematical Research Letters

## Volume 25 (2018)

### Number 3

### Iitaka’s $C_{n,m}$ conjecture for $3$-folds in positive characteristic

Pages: 783 – 802

DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n3.a3

#### Authors

#### Abstract

In this paper, we prove that for a fibration $f : X \to Z$ from a smooth projective $3$-fold to a smooth projective curve, over an algebraically closed field $k$ with $\mathrm{char}k = p \gt 5$, if the geometric generic fiber $X_{\overline{\eta}}$ is smooth, then subadditivity of Kodaira dimensions holds, i.e.\[\kappa (X) \geq \kappa (X_{\overline{\eta}}) + \kappa (Z) \; \textrm{.}\]

Received 16 April 2016

Accepted 2 March 2017

Published 3 August 2018