Automorphisms and examples of compact non Kähler manifolds

Gunnar Thór Magnússon (1)

1 IF - Institut Fourier

If f is an automorphism of a compact simply connected Kähler manifold with trivial canonical bundle that fixes a Kähler class, then the order of f is finite. We apply this well known result to construct compact non-Kähler manifolds. These manifolds contradict the abundance and Iitaka conjectures for complex manifolds.

Domaines: Géométrie algébrique [math.AG]

Gunnar Thór Magnússon. Automorphisms and examples of compact non Kähler manifolds. Mathematica Scandinavica, 2017, 121 (1), pp.49-56. ⟨10.7146/math.scand.a-25983⟩. ⟨hal-01680316⟩