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arXiv · 2606.27754

Locally Conformally K\"ahler Manifolds of Algebraic Codimension One

Liviu Ornea·Misha Verbitsky·Victor Vuletescu
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Abstract

A locally conformally K\"ahler (LCK) manifold is a manifold $M$ which admits a K\"ahler structure on its universal cover $\tilde M$, in such a way that the monodromy acts conformally on $\tilde M$. Let $M$ be an $n$-dimensional compact LCK manifold of algebraic dimension $n-1$. We prove that $M$ is bimeromorphic to the total space of an isotrivial elliptic fibration. Morever, there exists an alteration of $M$ which dominates bimeromorphically a manifold admitting a free action of an elliptic curve.

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Liviu Ornea, Misha Verbitsky, Victor Vuletescu. 2026-06-26. Locally Conformally K\"ahler Manifolds of Algebraic Codimension One. https://arxiv.org/abs/2606.27754

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