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Finite automorphism groups of hypersurfaces via Bott vanishing
Abstract
We give a cohomological criterion for the automorphism group scheme of a hypersurface in a smooth Deligne-Mumford stack to be discrete in tame characteristics. The criterion converts Bott-type vanishing on the ambient stack into vanishing of infinitesimal automorphisms of every quasismooth hypersurface in a linear system. We apply it to toric orbifolds, obtain uniform finiteness results for quasismooth weighted-projective hypersurfaces in tame characteristic and hypersurfaces in products of projective spaces, and identify the precise exceptional windows in which the method fails.
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BibTeX
@misc{bunnett2026finite,
title = {{Finite automorphism groups of hypersurfaces via Bott vanishing}},
author = {Dominic Bunnett and Caroline Namanya},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.38572},
eprint = {2609.38572},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.38572},
}
RIS
TY - UNPB
TI - Finite automorphism groups of hypersurfaces via Bott vanishing
AU - Dominic Bunnett
AU - Caroline Namanya
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.38572
UR - https://arxiv.org/abs/2609.38572
AB - We give a cohomological criterion for the automorphism group scheme of a hypersurface in a smooth Deligne-Mumford stack to be discrete in tame characteristics. The criterion converts Bott-type vanishing on the ambient stack into vanishing of infinitesimal automorphisms of every quasismooth hypersurface in a linear system. We apply it to toric orbifolds, obtain uniform finiteness results for quasismooth weighted-projective hypersurfaces in tame characteristic and hypersurfaces in products of projective spaces, and identify the precise exceptional windows in which the method fails.
ER -