2019 / September Volume 14 No.3
Asymptotics of torus equivariant Szegö kernel on a compact CR manifold
| Published Date |
2019 / September
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|---|---|
| Title | Asymptotics of torus equivariant Szegö kernel on a compact CR manifold |
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| Pagination | 331-383 |
| Abstract | For a compact CR manifold $(X,T^{1,0}X)$ of dimension $2n+1$, $n\geq 2$, admitting a $S^1\times T^d$ action, if the lattice point $(-p_1,\cdots,-p_d)\in\mathbb{Z}^{d}$ is a regular value of the
associate CR moment map $\mu$, then we establish the asymptotic expansion of the torus equivariant Szego kernel $\Pi^{(0)}_{m,mp_1,\cdots,mp_d}(x,y)$ as $m\to +\infty$ under certain assumptions of the positivity of Levi form and the torus action on $Y:=\mu^{-1}(-p_1,\cdots,-p_d)$.
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| DOI | |
| AMS Subject Classification |
2000 Mathematics Subject Classification. Primary: 32V20 ; Secondary: 35S30, 58J40
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| Received |
2018-10-15
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