A note on Iitaka's conjecture $C_{3,1}$ in positive characteristics

Abstract

Let $f:X\to Y$ be a fibration from a smooth projective 3-fold to a smooth projective curve, over an algebraically closed field $k$ of characteristic $p>5$. We prove that if the generic fiber $X_{\eta }$ has big canonical divisor $K_{X_{\eta }}$, then $$\kappa (X)\ge \kappa (Y)+\kappa (X_{\eta }).$$

14 pages, comments are welcome. to appear in Taiwanese J. Math

References in corpus (3)

• F-singularities in families
• On subadditivity of Kodaira dimension in positive characteristic
• On subadditivity of the logarithmic Kodaira dimension