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Polarized orbifolds associated to quantized Hamiltonian torus actions.
- Source :
-
Journal of Geometry & Physics . Dec2021, Vol. 170, pN.PAG-N.PAG. 1p. - Publication Year :
- 2021
-
Abstract
- Suppose given a holomorphic and Hamiltonian action of a compact torus T on a polarized Hodge manifold M. Assume that the action lifts to the quantizing line bundle, so that there is an induced unitary representation of T on the associated Hardy space. If in addition the moment map is nowhere zero, for each weight ν the ν -th isotypical component in the Hardy space of the polarization is finite-dimensional. Assuming that the moment map is transverse to the ray through ν , we give a geometric interpretation of the isotypical components associated to the weights k ν , k → + ∞ , in terms of certain polarized orbifolds associated to the Hamiltonian action and the weight. These orbifolds are generally not reductions of M in the usual sense, but arise rather as quotients of certain loci in the unit circle bundle of the polarization; this construction generalizes the one of weighted projective spaces as quotients of the unit sphere, viewed as the domain of the Hopf map. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 03930440
- Volume :
- 170
- Database :
- Academic Search Index
- Journal :
- Journal of Geometry & Physics
- Publication Type :
- Academic Journal
- Accession number :
- 153034589
- Full Text :
- https://doi.org/10.1016/j.geomphys.2021.104363