A Note on Iitaka's Conjecture $C_{3,1}$ in Positive Characteristics

Abstract

Let f : X → 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 η has big canonical divisor K Xη , then κ(X) ≥ κ(Y ) + κ(X η ).

Abundance for non‐uniruled 3‐folds with non‐trivial Albanese maps in positive characteristics

“…We collect some results which will be used in the sequel. For more general results on this topic please refer to [, , , , ]. Theorem Assume .…”

“…This approach was used in [12,Sec. 4] and [46]. In fact it applies once granted positivity results as in (1) without requiring X η to be smooth.…”