Uniformisation in dimension four: towards a conjecture of Iitaka

Details Uniformisation in dimension four: towards a conjecture of Iitaka Uniformisation in dimension four: towards a conjecture of Iitaka

2011-03-28

arxiv.org/abs/1103.5392v1

Mathematics

Algebraic Geometry

16 pages

Scientific paper

Let X be a compact K\"ahler manifold whose universal covering is C^n. A
conjecture of Iitaka claims that X is a torus, up to finite \'etale cover. We
prove this conjecture in various cases in dimension four. We also show that in
the projective case Iitaka's conjecture is a consequence of the non-vanishing
conjecture.

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