Journal of Symplectic Geometry

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

Mark D. Hamilton and Hiroshi Konno

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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.

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J. Symplectic Geom., Volume 12, Number 3 (2014), 473-509.

First available in Project Euclid: 29 August 2014

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Hamilton, Mark D.; Konno, Hiroshi. Convergence of Kähler to real polarizations on flag manifolds via toric degenerations. J. Symplectic Geom. 12 (2014), no. 3, 473--509.

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