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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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 29 August 2014

Permanent link to this document
https://projecteuclid.org/euclid.jsg/1409319458

Mathematical Reviews number (MathSciNet)
MR3248666

Zentralblatt MATH identifier
1300.32024

Citation

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. https://projecteuclid.org/euclid.jsg/1409319458


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