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Szegö kernels and finite group actions
Author(s):
Roberto
Paoletti
Journal:
Trans. Amer. Math. Soc.
356
(2004),
3069-3076.
MSC (2000):
Primary 14A10, 53D50, 57S17
Posted:
November 4, 2003
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Abstract:
In the context of almost complex quantization, a natural generalization of algebro-geometric linear series on a compact symplectic manifold has been proposed. Here we suppose given a compatible action of a finite group and consider the linear subseries associated to the irreducible representations of  , give conditions under which these are base-point-free and study properties of the associated projective morphisms. The results obtained are new even in the complex projective case.
References:
-
- [BU1]
- D. Borthwick, A. Uribe, Almost complex structures and geometric quantization, Math. Res. Lett. 3 (1996), 845-861. MR 98e:58084
- [BU2]
- D. Borthwick, A. Uribe, Nearly Kählerian embeddings of symplectic manifolds, Asian J. Math. 4 (2000), 599-620. MR 2001m:53166
- [BdM]
- L. Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure Appl. Math. 27 (1974), 585-639. MR 51:6498
- [BdMG]
- L. Boutet de Monvel, V. Guillemin, The spectral theory of Toeplitz operators, Ann. Math. Studies 99, Princeton University Press (1981). MR 85j:58141
- [GU]
- V. Guillemin, A. Uribe, The Laplace operators on the
 th tensor powers of a line-bundle, Asympt. Anal. 1 (1988), 105-113. MR 90a:58180 - [P]
- R. Paoletti, The asymptotic growth of equivariant sections of positive and big line bundles, preprint
- [SZ1]
- B. Shiffman, S. Zelditch, Universality and scaling of correlations between zeros on complex manifolds, Inv. Math. 142 (2000), 351-395. MR 2002f:32037
- [SZ2]
- B. Shiffman, S. Zelditch, Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds, J. Reine Angew. Math. 544 (2002), 181-222. MR 2002m:58043
- [S]
- S. Sternberg, Lectures on differential geometry, Prentice Hall, Englewood Cliffs, N.J. (1964). MR 33:1797
- [T]
- G. Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Diff. Geom. 32 (1990), 99-130. MR 91j:32031
- [Z]
- S. Zelditch, Szegö kernels and a theorem of Tian, Int. Math. Res. Notices 6 (1998), 317-331. MR 99g:32055
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Additional Information:
Roberto
Paoletti
Affiliation:
Dipartimento di Matematica e Applicazioni, Universitá di Milano Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
Email:
roberto.paoletti@unimib.it
DOI:
10.1090/S0002-9947-03-03490-1
PII:
S 0002-9947(03)03490-1
Received by editor(s):
January 10, 2003
Posted:
November 4, 2003
Copyright of article:
Copyright
2003,
American Mathematical Society
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