Bergman kernels on degenerations
Complex Variables
2023-04-28 v2 Algebraic Geometry
Differential Geometry
Abstract
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. We establish the continuity of the fiberwise Bergman kernel and provide a result on uniform convergence for the Fubini-Study currents. As a consequence, we show that the fiberwise Bergman kernel on test configurations exhibits continuity, and the Fubini-Study currents converge uniformly.
Cite
@article{arxiv.2304.01943,
title = {Bergman kernels on degenerations},
author = {Linsheng Wang and Shengxuan Zhou},
journal= {arXiv preprint arXiv:2304.01943},
year = {2023}
}
Comments
24 pages, some typos corrected