PreprintarXiv licencearXiv
Ampleness of non-symmetric line bundles on degenerations of abelian varieties
Abstract
Answering a 1985 question of Moret-Bailly, we prove by way of counterexample that if a line bundle ℒ on a degeneration of abelian varieties G → Spec(R) is not symmetric, then ℒ being ample on G is not necessarily equivalent to ℒ being ample on the generic fiber of G. Our technique of proof is to use the Fourier expansion principle for sections of line bundles on degenerations, due to Faltings--Chai and Lan.
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BibTeX
@misc{kallal2026ampleness,
title = {{Ampleness of non-symmetric line bundles on degenerations of abelian varieties}},
author = {Kenz Kallal},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26133},
eprint = {2610.26133},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26133},
}
RIS
TY - UNPB
TI - Ampleness of non-symmetric line bundles on degenerations of abelian varieties
AU - Kenz Kallal
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26133
UR - https://arxiv.org/abs/2610.26133
AB - Answering a 1985 question of Moret-Bailly, we prove by way of counterexample that if a line bundle ℒ on a degeneration of abelian varieties G → Spec(R) is not symmetric, then ℒ being ample on G is not necessarily equivalent to ℒ being ample on the generic fiber of G. Our technique of proof is to use the Fourier expansion principle for sections of line bundles on degenerations, due to Faltings--Chai and Lan.
ER -