Lower order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actionsReport as inadecuate



 Lower order asymptotics for Szegö and Toeplitz kernels under Hamiltonian circle actions


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We consider a natural variant of Berezin-Toeplitz quantization of compact K\-{a}hler manifolds, in the presence of a Hamiltonian circle action lifting to the quantizing line bundle. Assuming that the moment map is positive, we study the diagonal asymptotics of the associated Szeg\-{o} and Toeplitz operators, and specifically their relation to the moment map and to the geometry of a certain symplectic quotient. When the underlying action is trivial and the moment map is taken to be identically equal to one, this scheme coincides with the usual Berezin-Toeplitz quantization. This continues previous work on near-diagonal scaling asymptotics of equivariant Szeg\-{o} kernels in the presence of Hamiltonian torus actions.



Author: Roberto Paoletti

Source: https://archive.org/







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