Orbifold Iitaka Cnm conjecture

Let YY^\partial be a smooth or e-admissible effective orbifold, let g:YZg^\partial:Y^\partial\rightarrow Z be a fibration, and let YzY_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 XX^\partial be an e-admissible orbifold, let f:XYf:X^\partial\rightarrow Y be a morphism with effective orbifold base YY^\partial, let g:YZg:Y\dashrightarrow Z be meromorphic, and let h=gfh=g\circ f be almost holomorphic. Writing fz=fYzf_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.

Sources & referencesView supporting material

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.