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PreprintarXiv licencearXiv

Algebraic hyperbolicity of very general hypersurfaces in projective spaces

  • Sixuan Lou
  • Junyan Zhao
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Abstract

We prove that a very general sextic threefold in ℙ4 is algebraically hyperbolic, settling the last open case and completing the classification of algebraic hyperbolicity for very general hypersurfaces in projective space. The proof follows the Coskun--Riedl scroll construction, with the moduli of stable maps and the geometric canonical height as new ingredients.

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Cite

BibTeXRIS
BibTeX
@misc{lou2026algebraic,
  title = {{Algebraic hyperbolicity of very general hypersurfaces in projective spaces}},
  author = {Sixuan Lou and Junyan Zhao},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15628},
  eprint = {2609.15628},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15628},
}
RIS
TY  - UNPB
TI  - Algebraic hyperbolicity of very general hypersurfaces in projective spaces
AU  - Sixuan Lou
AU  - Junyan Zhao
PY  - 2026
DA  - 2026/09/16
PB  - arXiv
DO  - 10.48550/arxiv.2609.15628
UR  - https://arxiv.org/abs/2609.15628
AB  - We prove that a very general sextic threefold in ℙ^4 is algebraically hyperbolic, settling the last open case and completing the classification of algebraic hyperbolicity for very general hypersurfaces in projective space. The proof follows the Coskun--Riedl scroll construction, with the moduli of stable maps and the geometric canonical height as new ingredients.
ER  -