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Brane quantization of toric Poisson varieties. (English) Zbl 1492.53094

The paper under review concerns general compact toric varieties endowed with an invariant holomorphic Poisson structure induced by an R-matrix. The resulting algebra is a noncommutative deformation of the homogeneous coordinate ring of the underlying projective variety. In order to define the homomorphisms between generalized complex branes, this study uses a method which involves lifting each pair of generalized complex branes to a single coisotropic A-brane in the real symplectic groupoid of the given Poisson structure, and compute morphisms in the A-model between the Lagrangian identity bisection and the lifted coisotropic brane. This is obtained by using a multiplicative holomorphic Lagrangian polarization of the groupoid.

MSC:

53D17 Poisson manifolds; Poisson groupoids and algebroids
53D50 Geometric quantization
58H05 Pseudogroups and differentiable groupoids
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
22A22 Topological groupoids (including differentiable and Lie groupoids)
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