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Boundedness of geometrically integral ε-klt del Pezzo surfaces

  • Shikha Bhutani
  • Sudipta Das
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Abstract

We prove the remaining positive characteristic cases of the Borisov-Alexeev-Borisov conjecture for geometrically integral ε-klt del Pezzo surfaces over arbitrary fields. Bernasconi and Martin established boundedness outside characteristics $2$, $3$, and $5$, and reduced the remaining cases to a uniform bound for the irregularity. We prove this bound, thereby completing the boundedness theorem in all positive characteristics.

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Cite

BibTeXRIS
BibTeX
@misc{bhutani2026boundedness,
  title = {{Boundedness of geometrically integral $ε$-klt del Pezzo surfaces}},
  author = {Shikha Bhutani and Sudipta Das},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.24968},
  eprint = {2609.24968},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.24968},
}
RIS
TY  - UNPB
TI  - Boundedness of geometrically integral ε-klt del Pezzo surfaces
AU  - Shikha Bhutani
AU  - Sudipta Das
PY  - 2026
DA  - 2026/09/21
PB  - arXiv
DO  - 10.48550/arxiv.2609.24968
UR  - https://arxiv.org/abs/2609.24968
AB  - We prove the remaining positive characteristic cases of the Borisov-Alexeev-Borisov conjecture for geometrically integral ε-klt del Pezzo surfaces over arbitrary fields. Bernasconi and Martin established boundedness outside characteristics $2$, $3$, and $5$, and reduced the remaining cases to a uniform bound for the irregularity. We prove this bound, thereby completing the boundedness theorem in all positive characteristics.
ER  -