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LCK rank of locally conformally Kähler manifolds with potential
- Source :
- Journal of Geometry and Physics. 107:92-98
- Publication Year :
- 2016
- Publisher :
- Elsevier BV, 2016.
-
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.<br />14 pages. Supersedes arXiv:1512.00968. Contains errata to arXiv:math/0305259
- Subjects :
- Mathematics - Differential Geometry
Pure mathematics
Holomorphic function
General Physics and Astronomy
Kähler manifold
Rank (differential topology)
01 natural sciences
Mathematics - Algebraic Geometry
0103 physical sciences
FOS: Mathematics
0101 mathematics
Algebraic Geometry (math.AG)
Mathematics::Symplectic Geometry
Mathematical Physics
Quotient
Mathematics
Group (mathematics)
010102 general mathematics
Mathematical analysis
Manifold
Character (mathematics)
Differential Geometry (math.DG)
Monodromy
Mathematics::Differential Geometry
010307 mathematical physics
Geometry and Topology
Subjects
Details
- ISSN :
- 03930440
- Volume :
- 107
- Database :
- OpenAIRE
- Journal :
- Journal of Geometry and Physics
- Accession number :
- edsair.doi.dedup.....203c9f088a4665b570311aed50d30f5a