Seminar on Several Complex Variables

主講者: 沈威銓 (科隆大學)
講題: Asymptotics of torus equivariant Szegő kernel on a compact CR manifold.
時間: 2020-02-07 (Fri.)  10:30 - 12:00
地點: 數學所 722 研討室 (台大院區)
Abstract: In this talk, we consider a compact CR manifold $(X,T^{1,0}X)$ of dimension $2n+1$, $n\geq 2$, admitting a $S^1\times T^d$ action. We fix the lattice point $(p_1,\cdots,p_d)\in\mathbb{Z}^{d}$ satisfying $(-p_1,\cdots,-p_d)$ is a regular value of the associate CR moment map $\mu$ and study the asymptotic expansion of the corresponding torus equivariant Szegő kernel $\Pi^{(0)}_{m,mp_1,\cdots,mp_d}(x,y)$ as $m\to +\infty$ under certain assumptions on $Y:=\mu^{-1}(-p_1,\cdots,-p_d)$. As a corollary, we find a condition when the space of $R$-equivariant CR functions on a irregular Sasakian manifold is non-trivial in semi-classical limit.
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