Abstract:Let $({X}, \omega)$ 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 $-2\pi \sqrt{-1} \omega$. 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.
| Comments: | 33 pages |
| Subjects: | Differential Geometry (math.DG); Complex Variables (math.CV) |
| Cite as: | arXiv:2605.24572 [math.DG] |
| (or arXiv:2605.24572v1 [math.DG] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24572 arXiv-issued DOI via DataCite (pending registration) |
From: Julius Ross [view email]
[v1]
Sat, 23 May 2026 13:22:59 UTC (33 KB)
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