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arXiv · 2208.05833

Algebraic cones of LCK manifolds with potential

Liviu Ornea·Misha Verbitsky
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Abstract

A complex manifold $X$ is called "LCK manifolds with potential" if it can be realized as a complex submanifold of a Hopf manifold. Let $Y$ its $\Z$-covering, considered as a complex submanifold in $C^n \backslash 0$. We prove that $Y$ is algebraic. We call the manifolds obtained this way the algebraic cones, and show that the affine algebraic structure on $Y$ is independent from the choice of $X$. We give several intrinsic definitions of an algebraic cone, and prove that these definitions are equivalent.

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Liviu Ornea, Misha Verbitsky. 2022-08-11. Algebraic cones of LCK manifolds with potential. https://doi.org/10.1016/j.geomphys.2024.105103

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