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arXiv · 2605.24572

Orbifold Bergman Kernels

Julius Ross·Shin Kim
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Abstract

Let $({X}, ω)$ be a compact $n$-dimensional Kähler orbifold, the stabilizer groups of which are abelian and have rank at most two. Let ${E}$ be an orbi-ample vector bundle of rank $2$ over ${X}$ and let $H$ be a Hermitian metric on ${E}$ such that the curvature form of $\det H$ is $-2π\sqrt{-1} ω$. We show that a certain weighted sum of Bergman kernels for ${Sym}^i {E} \otimes \det({E})^{k+j}$ as $i$ and $j$ vary over a finite set admit an asymptotic expansion. This extends a similar result for cyclic Kähler orbifolds.

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Julius Ross, Shin Kim. 2026-05-23. Orbifold Bergman Kernels. https://arxiv.org/abs/2605.24572

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