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PreprintarXiv licencearXiv

Bound of automorphisms of fibred surfaces in positive characteristic

  • Xiaokun Zhong
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Abstract

Let f : S → B be a fibred surface over an algebraically closed field k of characteristic p ≥ 5, where S is a minimal smooth projective surface of general type and B is a smooth projective curve of genus b≥ 2. We prove that the group of fibration-preserving automorphisms of f has order at most 15658(KS2)4. Furthermore, we provide an example to show that the exponent $4$ of the polynomial bound is sharp.

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Cite

BibTeXRIS
BibTeX
@misc{zhong2026bound,
  title = {{Bound of automorphisms of fibred surfaces in positive characteristic}},
  author = {Xiaokun Zhong},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21485},
  eprint = {2609.21485},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21485},
}
RIS
TY  - UNPB
TI  - Bound of automorphisms of fibred surfaces in positive characteristic
AU  - Xiaokun Zhong
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21485
UR  - https://arxiv.org/abs/2609.21485
AB  - Let f : S → B be a fibred surface over an algebraically closed field k of characteristic p ≥ 5, where S is a minimal smooth projective surface of general type and B is a smooth projective curve of genus b≥ 2. We prove that the group of fibration-preserving automorphisms of f has order at most 15658(K_S^2)^4. Furthermore, we provide an example to show that the exponent $4$ of the polynomial bound is sharp.
ER  -