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

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 $\mathrm{char}k=p>5$, if the geometric generic fiber $X_{\overline{\eta }}$ is smooth, then subadditivity of Kodaira dimensions holds, i.e. $$\kappa (X)\ge \kappa (X_{\overline{\eta }})+\kappa (Z).$$

14 pages, v2: minor revisions, v3: Correction of the proof of the main theorem for the case where the Kodaira dimension of the generic fiber is one. v4: final version, to appear in Math. Res. Lett, v5: References corrected

References in corpus (1)

• The LMMP for log canonical 3-folds in char $p$