Geometry and topology · Oct 6, 2026

Iitaka subadditivity, variation, and logarithmic additivity

Proves Campana's orbifold Iitaka subadditivity conjecture for smooth Fujiki-class-

\mathcal C

manifolds with rational simple-normal-crossing boundaries. For projective fibrations

f:U\to V

of smooth complex quasi-projective varieties with connected fibers, general fiber F, and

\bar\kappa(V)\ge0

, proves Popa's inequality

\bar\kappa(U)\ge\kappa(F)+\max\{\bar\kappa(V),\mathop{\mathrm{Var}}\nolimits (f)\}

, where variation measures the whole geometric generic fiber.

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