Viehweg's conjecture C(n,m)+ and Popa's logarithmic Iitaka-Viehweg inequality

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Viehweg's conjecture C(n,m)+ and Popa's logarithmic Iitaka-Viehweg inequality parent of this event

Popa's logarithmic additivity conjecture for log-smooth families evidence for this event

Orbifold and logarithmic Iitaka subadditivity evidence for this event

Popa, Conjectures on the Kodaira dimension (author version) evidence for this event

Viehweg's conjecture C(n,m)+ and Popa's logarithmic Iitaka-Viehweg inequality evidence for this event

Theorem 1.1: for a projective surjective morphism $f:U\to V$ with connected fibres between smooth connected complex quasi-projective varieties with $\bar\kappa(V)\ge0$ and geometric generic fibre $F$, $\bar\kappa(U)\ge\kappa(F)+\max\{\bar\kappa(V),\mathrm{Var}(f)\}$, with no good-minimal-model or abundance hypothesis on $F$. Corollary 1.2 gives Viehweg's ordinary $C^+_{n,m}$ for projective complex fibre spaces with $\kappa(Y)\ge0$. Not covered: bases with $\bar\kappa(V)=-\infty$, positive characteristic, and the additivity equalities for smooth families (a separate entry). parent of this event

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