Convergence of Kähler to real polarizations on flag manifolds via toric degenerations

In this paper, we construct a family of complex structures on a complex flag manifold that converge to the real polarization coming from the Gelfand–Cetlin integrable system, in the sense that holomorphic sections of a prequantum line bundle converge to delta-function sections supported on the Bohr–...

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Bibliographic Details
Published in:Journal of symplectic geometry 2014, Vol.12 (3), p.473-509
Main Authors: Hamilton, Mark D., Konno, Hiroshi
Format: Article
Language:English
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Summary:In this paper, we construct a family of complex structures on a complex flag manifold that converge to the real polarization coming from the Gelfand–Cetlin integrable system, in the sense that holomorphic sections of a prequantum line bundle converge to delta-function sections supported on the Bohr–Sommerfeld fibers. Our construction is based on a toric degeneration of flag varieties and a deformation of Kähler structure on toric varieties by symplectic potentials.
ISSN:1527-5256
1540-2347
DOI:10.4310/JSG.2014.v12.n3.a3