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Bergman kernels on degenerations
Linsheng Wang, Shengxuan Zhou
We introduce the fiberwise Bergman kernel for a flat family of polarized varieties over a Riemann surface, which extends the classical Bergman kernel defined on the reduced fibers.…
Peak sections and Bergman kernels on Kähler manifolds with complex hyperbolic cusps
Shengxuan Zhou
By revisiting Tian's peak section method, we obtain a localization principle of the Bergman kernels on Kähler manifolds with complex hyperbolic cusps, which is a generalization of…
On the convergence rate of Bergman metrics
Shengxuan Zhou
We study the convergence rate of Bergman metrics on the class of polarized pointed Kähler -manifolds with and $|\sec |\leq K…
The asymptotic behaviour of Bergman kernels
Shengxuan Zhou
Let be the pointed Gromov-Hausdorff limit of a sequence of pointed complete polarized Kähler manifolds with $Ric ( h_l ) =2π…