The generalized Iitaka conjecture for klt pairs

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Let (X,B)(X,B) be a projective klt pair with BB a QQ-boundary, and let f ⁣:X→Zf\colon X\to Z be an algebraic fibre space onto a smooth projective variety ZZ. Let FF be a general fibre of ff, and define

KF+BF:=(KX+B)∣F.K_F+B_F:=(K_X+B)|_F.

Generalized Iitaka conjecture. One has

κ(KX+B)≥κ(KF+BF)+κ(Z).\kappa(K_X+B)\geq \kappa(K_F+B_F)+\kappa(Z).

This is a generalized form of the Iitaka conjecture for the Kodaira dimension of a log pair, extending the expected subadditivity inequality from varieties to klt pairs. The source presents it after proving a special case for bases of maximal Albanese dimension; its general validity is not established here.

References

Primary source

Caucher Birkar and Jungkai Alfred Chen, “Varieties fibred over abelian varieties with fibres of log general type”, arXiv:1311.7396 (2013).

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