For a surjective connected-fiber holomorphic map from a smooth compact connected Fujiki-class-C manifold with rational simple-normal-crossing boundary to a normal compact irreducible complex space, the total log Kodaira dimension is at least the sum of the very general fiber log Kodaira dimension and Campana’s orbifold-base Kodaira dimension, including boundary coefficient one.
For a surjective connected-fiber holomorphic map from a smooth compact connected Fujiki-class-C manifold with rational simple-normal-crossing boundary to a normal compact irreducible complex space, the total log Kodaira dimension is at least the sum of the very general fiber log Kodaira dimension and Campana’s orbifold-base Kodaira dimension, including boundary coefficient one.
For a surjective connected-fiber holomorphic map from a smooth compact connected Fujiki-class-C manifold with rational simple-normal-crossing boundary to a normal compact irreducible complex space, the total log Kodaira dimension is at least the sum of the very general fiber log Kodaira dimension and Campana’s orbifold-base Kodaira dimension, including boundary coefficient one.
If correct, resolves Campana’s rational-SNC orbifold Iitaka subadditivity conjecture and yields ordinary and logarithmic subadditivity as consequences.
Does the total log Kodaira dimension dominate the fiber and orbifold-base dimensions for the stated fibrations?
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