Szegö kernels and finite group actions

Paoletti, Roberto

doi:10.1090/S0002-9947-03-03490-1

Szegö kernels and finite group actions
HTML articles powered by AMS MathViewer

by Roberto Paoletti PDF

Trans. Amer. Math. Soc. 356 (2004), 3069-3076 Request permission

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 $G$, 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

David Borthwick and Alejandro Uribe, Almost complex structures and geometric quantization, Math. Res. Lett. 3 (1996), no. 6, 845–861. MR 1426541, DOI 10.4310/MRL.1996.v3.n6.a12
David Borthwick and Alejandro Uribe, Nearly Kählerian embeddings of symplectic manifolds, Asian J. Math. 4 (2000), no. 3, 599–620. MR 1796696, DOI 10.4310/AJM.2000.v4.n3.a6
Louis Boutet de Monvel, Hypoelliptic operators with double characteristics and related pseudo-differential operators, Comm. Pure Appl. Math. 27 (1974), 585–639. MR 370271, DOI 10.1002/cpa.3160270502
L. Boutet de Monvel and V. Guillemin, The spectral theory of Toeplitz operators, Annals of Mathematics Studies, vol. 99, Princeton University Press, Princeton, NJ; University of Tokyo Press, Tokyo, 1981. MR 620794, DOI 10.1515/9781400881444
V. Guillemin and A. Uribe, The Laplace operator on the $n$th tensor power of a line bundle: eigenvalues which are uniformly bounded in $n$, Asymptotic Anal. 1 (1988), no. 2, 105–113. MR 950009, DOI 10.3233/ASY-1988-1202
R. Paoletti, The asymptotic growth of equivariant sections of positive and big line bundles, preprint
Pavel Bleher, Bernard Shiffman, and Steve Zelditch, Universality and scaling of correlations between zeros on complex manifolds, Invent. Math. 142 (2000), no. 2, 351–395. MR 1794066, DOI 10.1007/s002220000092
Bernard Shiffman and Steve Zelditch, Asymptotics of almost holomorphic sections of ample line bundles on symplectic manifolds, J. Reine Angew. Math. 544 (2002), 181–222. MR 1887895, DOI 10.1515/crll.2002.023
Shlomo Sternberg, Lectures on differential geometry, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1964. MR 0193578
Gang Tian, On a set of polarized Kähler metrics on algebraic manifolds, J. Differential Geom. 32 (1990), no. 1, 99–130. MR 1064867
Steve Zelditch, Szegő kernels and a theorem of Tian, Internat. Math. Res. Notices 6 (1998), 317–331. MR 1616718, DOI 10.1155/S107379289800021X