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Equivariant asymptotics of Szegö kernels under Hamiltonian \({{\varvec{U}}}(\mathbf{2})\)-actions

  • Andrea Galasso
  • Roberto PaolettiEmail author
Article
  • 25 Downloads

Abstract

Let M be complex projective manifold and A a positive line bundle on it. Assume that a compact and connected Lie group G acts on M in a Hamiltonian manner and that this action linearizes to A. Then, there is an associated unitary representation of G on the associated algebro-geometric Hardy space. If the moment map is nowhere vanishing, the isotypical components are all finite dimensional; they are generally not spaces of sections of some power of A. One is then led to study the local and global asymptotic properties the isotypical component associated with a weight \(k \, \varvec{ \nu }\), when \(k\rightarrow +\infty \). In this paper, part of a series dedicated to this general theme, we consider the case \(G=U(2)\).

Keywords

Hamiltonian action Positive line bundle Szegö kernel Hardy space Asymptotic expansion 

Mathematics Subject Classification

30H10 32M05 53D20 53D35 53D50 57S15 

Notes

Acknowledgements

We thank the referee for suggesting some improvements in presentations.

Funding Funding was supported by Università degli Studi di Milano Bicocca (IT) (Grant No. 2014-ATE-0080).

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica e ApplicazioniUniversità degli Studi di Milano BicoccaMilanItaly

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