Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds

2021/08/29 by Tiba, Yusaku
#32Q15 #53D12 #53D50 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.01492

Abstract

Let M be a complex manifold and L be a line bundle over M with a Hermitian metric h whose Chern form is a Kähler form ω. Let X ⊂ M be a Lagrangian submanifold of (M, ω). When X satisfies the Bohr-Sommerfeld condition, we give an asymptotic estimate of the norm |f|_h^k on X for f ∈ H⁰(M, L^k).

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