  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.
