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

Abstract

In this paper, we prove abundance for non‐uniruled 3‐folds with non‐trivial Albanese maps, over an algebraically closed field of characteristic p>5. As an application we get a characterization of abelian 3‐folds.

Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics

“…(3) Varieties of maximal Albanese dimension are non-uniruled. The results in this paper can be applied to study abundance for 3-folds with dim Pic 0 (X) > 0, which is finally proved in a later paper [51].…”

On the Abundance Problem for $3$-folds in characteristic $p>5$

“…We were informed that similar results were obtained independently around the same time by Zhang in [Zha17]; however our techniques seem to be different from his.…”

Birational characterization of Abelian varieties and ordinary Abelian varieties in characteristic p>0

“…(1) F ∼ = (Ω Xreg /G| Xreg ) * ⇒ det F = det G − K X , and (2) as by [S58,Théorème 4] the natural map H 0 (A, Ω A ) → H 0 (X, Ω X ) is an injection, and G is generically generated by a dim H 0 (X, G) > rk G dimensional section space, κ(det G) > 0 [Z16,Lemma 4.2].…”