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 kν, when k→ + ∞. In this paper, part of a series dedicated to this general theme, we consider the case G= U(2).

Galasso, A., Paoletti, R. (2019). Equivariant asymptotics of Szegö kernels under Hamiltonian U(2) -actions. ANNALI DI MATEMATICA PURA ED APPLICATA, 198(2), 639-683 [10.1007/s10231-018-0791-3].

Equivariant asymptotics of Szegö kernels under Hamiltonian U(2) -actions

Galasso, A;Paoletti, R
2019

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 kν, when k→ + ∞. In this paper, part of a series dedicated to this general theme, we consider the case G= U(2).
Articolo in rivista - Articolo scientifico
Asymptotic expansion; Hamiltonian action; Hardy space; Positive line bundle; Szegö kernel;
Asymptotic expansion; Hamiltonian action; Hardy space; Positive line bundle; Szegö kernel; Applied Mathematics
English
2018
2019
198
2
639
683
partially_open
Galasso, A., Paoletti, R. (2019). Equivariant asymptotics of Szegö kernels under Hamiltonian U(2) -actions. ANNALI DI MATEMATICA PURA ED APPLICATA, 198(2), 639-683 [10.1007/s10231-018-0791-3].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/222700
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