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PreprintCC BY 4.0arXiv

Class VII surfaces with b2=3 and two foliations are Kato

  • Nikon Kurnosov
  • Calum Spicer
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Abstract

Let S be a minimal compact complex surface of class VII with b2(S)=3. We prove that if S carries two distinct singular holomorphic foliations, then S contains a global spherical shell. Moreover, it is an Inoue-Hirzebruch surface. The proof is based on Teleman's theorem on the existence of a cycle of rational curves and results of Dloussky and is inspired by work of Brunella.

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Cite

BibTeXRIS
BibTeX
@misc{kurnosov2026class,
  title = {{Class VII surfaces with $b_2=3$ and two foliations are Kato}},
  author = {Nikon Kurnosov and Calum Spicer},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29047},
  eprint = {2608.29047},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29047},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Class VII surfaces with b_2=3 and two foliations are Kato
AU  - Nikon Kurnosov
AU  - Calum Spicer
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29047
UR  - https://arxiv.org/abs/2608.29047
AB  - Let S be a minimal compact complex surface of class VII with b_2(S)=3. We prove that if S carries two distinct singular holomorphic foliations, then S contains a global spherical shell. Moreover, it is an Inoue-Hirzebruch surface. The proof is based on Teleman's theorem on the existence of a cycle of rational curves and results of Dloussky and is inspired by work of Brunella.
ER  -