Bergman kernels on degenerations
Copyright policy )Bergman kernels on degenerations
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.
24 pages, some typos corrected
- Peking University China (People's Republic of)
- Fudan University China (People's Republic of)
flat families, Mathematics - Differential Geometry, Riemann surfaces, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), FOS: Mathematics, Global differential geometry of Hermitian and Kählerian manifolds, Bergman kernels, Complex Variables (math.CV), Kähler manifolds, Algebraic Geometry (math.AG)
flat families, Mathematics - Differential Geometry, Riemann surfaces, Mathematics - Algebraic Geometry, Differential Geometry (math.DG), Mathematics - Complex Variables, Integral representations; canonical kernels (Szegő, Bergman, etc.), FOS: Mathematics, Global differential geometry of Hermitian and Kählerian manifolds, Bergman kernels, Complex Variables (math.CV), Kähler manifolds, Algebraic Geometry (math.AG)
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