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Automorphisms of ℙ1-bundles over rational surfaces in positive characteristic

  • Jérémy Blanc
  • Ronan Terpereau
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Abstract

We study ℙ1-bundles over smooth projective rational surfaces over an algebraically closed field of characteristic p>0, together with the actions of their neutral automorphism groups. After an equivariant square birational reduction to the projective plane or a Hirzebruch surface, we classify the possible induced actions on the base and identify the families relevant to relative maximality. For p≥ 3, we prove that every such ℙ1-bundle is equivariantly square birational to one whose neutral automorphism group is relatively maximal, and we classify all bundles with this property. We also describe all equivariant square birational maps between these relatively maximal bundles and determine which are stiff or superstiff, the analogues of rigidity and superrigidity for ℙ1-bundles.

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Cite

BibTeXRIS
BibTeX
@misc{blanc2026automorphisms,
  title = {{Automorphisms of $\mathbbP^1$-bundles over rational surfaces in positive characteristic}},
  author = {Jérémy Blanc and Ronan Terpereau},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.35024},
  eprint = {2610.35024},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.35024},
}
RIS
TY  - UNPB
TI  - Automorphisms of ℙ^1-bundles over rational surfaces in positive characteristic
AU  - Jérémy Blanc
AU  - Ronan Terpereau
PY  - 2026
DA  - 2026/10/26
PB  - arXiv
DO  - 10.48550/arxiv.2610.35024
UR  - https://arxiv.org/abs/2610.35024
AB  - We study ℙ^1-bundles over smooth projective rational surfaces over an algebraically closed field of characteristic p>0, together with the actions of their neutral automorphism groups. After an equivariant square birational reduction to the projective plane or a Hirzebruch surface, we classify the possible induced actions on the base and identify the families relevant to relative maximality. For p≥ 3, we prove that every such ℙ^1-bundle is equivariantly square birational to one whose neutral automorphism group is relatively maximal, and we classify all bundles with this property. We also describe all equivariant square birational maps between these relatively maximal bundles and determine which are stiff or superstiff, the analogues of rigidity and superrigidity for ℙ^1-bundles.
ER  -