Abstract
In this paper, we will prove subadditivity of Kodaira dimensions for a fibration with possibly singular geometric generic fiber, under certain nefness and relative semi-ampleness conditions. As an application, for a fibration f:X→Y of a smooth projective threefold over an algebraically closed field of characteristic p>5, under the assumption that Y is of general type and non-uniruled, we prove subadditivity of Kodaira dimensions when general fibers are smooth or when KX/Y is relatively big over Y.
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