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International Press, Journal of Symplectic Geometry, 3(12), p. 473-509

DOI: 10.4310/jsg.2014.v12.n3.a3

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

Journal article published in 2014 by Mark D. Hamilton, Hiroshi Konno
This paper is made freely available by the publisher.
This paper is made freely available by the publisher.

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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.