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arXiv · 1601.07413

LCK rank of locally conformally Kahler manifolds with potential

Liviu Ornea·Misha Verbitsky
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Abstract

An LCK manifold with potential is a compact quotient of a Kahler manifold $X$ equipped with a positive Kahler potential $f$, such that the monodromy group acts on $X$ by holomorphic homotheties and multiplies $f$ by a character. The LCK rank is the rank of the image of this character, considered as a function from the monodromy group to real numbers. We prove that an LCK manifold with potential can have any rank between 1 and $b_1(M)$. Moreover, LCK manifolds with proper potential (ones with rank 1) are dense. Two errata to our previous work are given in the last Section.

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BibTeXRIS

Liviu Ornea, Misha Verbitsky. 2016-01-27. LCK rank of locally conformally Kahler manifolds with potential. https://doi.org/10.1016/j.geomphys.2016.05.011

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