Equidistribution for semiabelian varieties over number fields
Abstract
K{ü}hne established equidistribution for canonical adelic line bundles on semiabelian varieties, a setting which need not lie in the quasi-canonical range of Yuan-Zhang's theorem. We study adelic line bundles on semiabelian compactifications whose toric part is governed by a toric metrized divisor. The main unconditional result is generic equidistribution when the toric metric is monocritical and arithmetically T-effective. The proof isolates the asymptotic estimates in K{ü}hne's argument and reinterprets them as estimates along explicit compression paths. This gives a comparison mechanism between canonical, quasi-canonical, and more general toric metrics. For the Bogomolov application, the quasi-canonical case is handled by a K{ü}hne local-trivialization transport package. After fixing a single theta-factor convention for the local trivializations, the proof checks the Picard-zero theta factors under K{ü}hne's operations and obtains the Bogomolov theorem for the metric class treated in this paper, namely the monocritical and arithmetically T-effective toric metrics, through the quasi-canonical replacement argument.
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BibTeX
@misc{xue2026equidistribution,
title = {{Equidistribution for semiabelian varieties over number fields}},
author = {Wei Xue},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.08262},
eprint = {2608.08262},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.08262},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Equidistribution for semiabelian varieties over number fields
AU - Wei Xue
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.08262
UR - https://arxiv.org/abs/2608.08262
AB - K{ü}hne established equidistribution for canonical adelic line bundles on semiabelian varieties, a setting which need not lie in the quasi-canonical range of Yuan-Zhang's theorem. We study adelic line bundles on semiabelian compactifications whose toric part is governed by a toric metrized divisor. The main unconditional result is generic equidistribution when the toric metric is monocritical and arithmetically T-effective. The proof isolates the asymptotic estimates in K{ü}hne's argument and reinterprets them as estimates along explicit compression paths. This gives a comparison mechanism between canonical, quasi-canonical, and more general toric metrics. For the Bogomolov application, the quasi-canonical case is handled by a K{ü}hne local-trivialization transport package. After fixing a single theta-factor convention for the local trivializations, the proof checks the Picard-zero theta factors under K{ü}hne's operations and obtains the Bogomolov theorem for the metric class treated in this paper, namely the monocritical and arithmetically T-effective toric metrics, through the quasi-canonical replacement argument.
ER -