Abstract: A Hermitian manifold is locally conformally Kaehler (LCK) if it admits a Kaehler cover on which the deck group acts by homotheties.
If this Kaehler metric has a positive, global potential, the manifold is called LCK with potential. The typical example is the Hopf manifold which is clearly non-algebraic. However, we prove that the coverings of LCK manifolds with potential have an algebraic structure, being in fact affine cones over projective orbifolds.
This permits using algebraic geometry techniques in the study of non-algebraic manifolds.
The material that I shall present belongs to joint works with Misha Verbitsky.
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