Orbifold Bergman Kernels
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911713370046464 |
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| author | Ross, Julius Kim, Shin |
| author_facet | Ross, Julius Kim, Shin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24572 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbifold Bergman Kernels Ross, Julius Kim, Shin Differential Geometry Complex Variables 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. |
| title | Orbifold Bergman Kernels |
| topic | Differential Geometry Complex Variables |
| url | https://arxiv.org/abs/2605.24572 |