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Asymptotics of holomorphic torsion on orbifolds and an equivariant arithmetic Hilbert-Samuel theorem
Abstract
We compute the log p-part of the asymptotic expansion of the holomorphic torsion of the p-th power of a positive line bundle in terms of characteristic classes. This is done for orbifold and equivariant torsions. In the equivariant case the exponents in the expansion are less than or equal to the dimension of the fixed point set. We deduce a corresponding equivariant arithmetic Hilbert-Samuel theorem in Arakelov geometry.
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BibTeX
@misc{kohler2026asymptotics,
title = {{Asymptotics of holomorphic torsion on orbifolds and an equivariant arithmetic Hilbert-Samuel theorem}},
author = {Kai Köhler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02192},
eprint = {2609.02192},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02192},
}
RIS
TY - UNPB
TI - Asymptotics of holomorphic torsion on orbifolds and an equivariant arithmetic Hilbert-Samuel theorem
AU - Kai Köhler
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02192
UR - https://arxiv.org/abs/2609.02192
AB - We compute the log p-part of the asymptotic expansion of the holomorphic torsion of the p-th power of a positive line bundle in terms of characteristic classes. This is done for orbifold and equivariant torsions. In the equivariant case the exponents in the expansion are less than or equal to the dimension of the fixed point set. We deduce a corresponding equivariant arithmetic Hilbert-Samuel theorem in Arakelov geometry.
ER -