Weak positivity theorem and Frobenius stable canonical rings of geometric generic fibers

Abstract

In this paper, we prove the weak positivity theorem in positive characteristic when the canonical ring of the geometric generic fiber $F$ is finitely generated and the Frobenius stable canonical ring of $F$ is large enough. As its application, we show the subadditivity of Kodaira dimensions in some new cases.

33 pages, v2: the numbering of theorems and corollaries in Section 3 are changed, Corollary 5.4 (ii) was removed due to an error in the proof, the assumption of Theorem 6.8 is strengthened due to an error similar to the above, to appear in J. Algebraic Geom

References in corpus (4)

• Semipositivity theorems for moduli problems
• F-singularities in families
• On subadditivity of Kodaira dimension in positive characteristic
• Some remarks on the semi-positivity theorems