Asymptotics for Bergman projections with smooth weights: a direct approach

2021/05/30 by Michael Hitrik, Hitrik, Michael, Matthew Stone +1 · 1 citation
Mathematics · #32A25 #32W05 #32W25 #35S30 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.CV #math.FA #msc:32A25 #msc:32W05 #msc:32W25 #msc:35S30

paper · pdf · doi:10.48550/arxiv.2105.14402

arxiv created 2021/05/30 · arxiv updated 2021/06/01

Abstract

We adapt the direct approach to the semiclassical Bergman kernel asymptotics, developed recently by A. Deleporte, J. Sjöstrand, and the first-named author for real analytic exponential weights, to the smooth case. Similar to that work, our approach avoids the use of the Kuranishi trick and it allows us to construct the amplitude of the asymptotic Bergman projection by means of an asymptotic inversion of an explicit Fourier integral operator.

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• Bergman kernels over polarized Kähler manifolds, Bergman logarithmic flatness, and a question of Lu-Tian

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