Kirwin, William D., Mourao, Jose M. and Nunes, Joao P. (2016). Complex symplectomorphisms and pseudo-Kahler islands in the quantization of toric manifolds. Math. Ann., 364 (1-2). S. 1 - 29. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1807
Full text not available from this repository.Abstract
Let P be a Delzant polytope. We show that the quantization of the corresponding toric manifold X-P in toric Kahler polarizations and in the toric real polarization are related by analytic continuation of Hamiltonian flows evaluated at time t = root-1s. We relate the quantization of X-P in two different toric Kahler polarizations by taking the time t = root-1s Hamiltonian flow of strongly convex functions on the moment polytope P. By taking s to infinity, we obtain the quantization of X-P in the (singular) real toric polarization. Recall that X-P has an open dense subset which is biholomorphic to (C*)(n). The quantization of X-P in a toric Kahler polarization can also be described by applying the complexified Hamiltonian flow of the Abreu-Guillemin symplectic potential g, at time t = root-1, to an appropriate finite-dimensional subspace of quantum states in the quantization of T*T-n in the vertical polarization. By taking other imaginary times, t = k root-1, k is an element of R, we describe toric Kahler metrics with cone singularities along the toric divisors in X-P. For convex Hamiltonian functions and sufficiently negative imaginary part of the complex time, we obtain degenerate Kahler structures which are negative definite in some regions of X-P. We show that the pointwise and L-2-norms of quantum states are asymptotically vanishing on negative-definite regions.
Item Type: | Journal Article | ||||||||||||||||
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URN: | urn:nbn:de:hbz:38-284917 | ||||||||||||||||
DOI: | 10.1007/s00208-015-1205-0 | ||||||||||||||||
Journal or Publication Title: | Math. Ann. | ||||||||||||||||
Volume: | 364 | ||||||||||||||||
Number: | 1-2 | ||||||||||||||||
Page Range: | S. 1 - 29 | ||||||||||||||||
Date: | 2016 | ||||||||||||||||
Publisher: | SPRINGER HEIDELBERG | ||||||||||||||||
Place of Publication: | HEIDELBERG | ||||||||||||||||
ISSN: | 1432-1807 | ||||||||||||||||
Language: | English | ||||||||||||||||
Faculty: | Unspecified | ||||||||||||||||
Divisions: | Unspecified | ||||||||||||||||
Subjects: | no entry | ||||||||||||||||
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Refereed: | Yes | ||||||||||||||||
URI: | http://kups.ub.uni-koeln.de/id/eprint/28491 |
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