Compact LCK n-manifolds with algebraic dimension n-1 are bimeromorphic to isotrivial elliptic fibrations, and an alteration of M dominates bimeromorphically a manifold with free elliptic curve action.
ahler surfaces and locally conformally K\
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Locally Conformally K\"ahler Manifolds of Algebraic Codimension One
Compact LCK n-manifolds with algebraic dimension n-1 are bimeromorphic to isotrivial elliptic fibrations, and an alteration of M dominates bimeromorphically a manifold with free elliptic curve action.