Orbifold Iitaka Cnm conjecture

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Let Y∂Y^\partial be a smooth or e-admissible effective orbifold, let g∂:Y∂→Zg^\partial:Y^\partial\rightarrow Z be a fibration, and let Yz∂Y_z^\partial be its orbifold general fiber. Orbifold Iitaka Cnm conjecture. One has

κ(Y∂)≥κ(Yz∂)+κ(Z,g∂).\kappa(Y^\partial)\geq \kappa(Y_z^\partial)+\kappa(Z,g^\partial).

More generally, let X∂X^\partial be an e-admissible orbifold, let f:X∂→Yf:X^\partial\rightarrow Y be a morphism with effective orbifold base Y∂Y^\partial, let g:Y⇢Zg:Y\dashrightarrow Z be meromorphic, and let h=g∘fh=g\circ f be almost holomorphic. Writing fz=f∣Yzf_z=f|_{Y_z}, one has

κ(Y,f∂)≥κ(Yz,fz∂)+κ(Z,h∂).\kappa(Y,f^\partial)\geq \kappa(Y_z,f_z^\partial)+\kappa(Z,h^\partial).

This is the orbifold generalization of Iitaka's subadditivity conjecture for Kodaira dimensions; the supplied text does not give a resolution status.

References

Primary source

Steven S. Y. Lu, “A refined Kodaira dimension and its canonical fibration”, arXiv:math/0211029 (2002).

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