Advanced Studies in Pure Mathematics

Complex and Kähler structures on compact homogeneous manifolds—their existence, classification and moduli problem

Keizo Hasegawa

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Abstract

We will survey basic results and recent progress in the existence, classification and moduli problems of complex and Kähler structures on compact homogeneous manifolds. We also state and discuss some related conjectures for further study in this field.

Article information

Source
Singularities — Niigata–Toyama 2007, J.-P. Brasselet, S. Ishii, T. Suwa and M. Vaquie, eds. (Tokyo: Mathematical Society of Japan, 2009), 151-167

Dates
Received: 21 January 2008
Revised: 15 April 2008
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543448016

Digital Object Identifier
doi:10.2969/aspm/05610151

Mathematical Reviews number (MathSciNet)
MR2604081

Zentralblatt MATH identifier
1195.32014

Subjects
Primary: 32M10: Homogeneous complex manifolds [See also 14M17, 57T15] 53C30: Homogeneous manifolds [See also 14M15, 14M17, 32M10, 57T15] 53C55: Hermitian and Kählerian manifolds [See also 32Cxx] 22E25: Nilpotent and solvable Lie groups

Keywords
Complex structure Kähler structure homogeneous manifold

Citation

Hasegawa, Keizo. Complex and Kähler structures on compact homogeneous manifolds—their existence, classification and moduli problem. Singularities — Niigata–Toyama 2007, 151--167, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05610151. https://projecteuclid.org/euclid.aspm/1543448016


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