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Regular version of the site

Article

LCK rank of locally conformally Kähler manifolds with potential

Journal of Geometry and Physics. 2016. Vol. 107. P. 92-98.
Ornea L., Verbitsky M.

An LCK manifold with potential is a compact quotient of a Kähler manifold X equipped with a positive Kähler 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 b1(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.