On n-dimensional compact Kähler manifolds covered by Cⁿ

Mihai Paun

Strasbourg, France

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Abstract

We report on a joint work in progress with F. Campana. Consider X a compact Kähler manifold, such that its canonical

is nef. Assume also that there exist a holomorphic map from Cⁿ to X, whose Jacobian is not identically zero. We prove

that in some cases such a manifold has numerically trivial canonical bundle.