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Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts

  • Bjoern Hassfeld
  • Jakob Moritz
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Abstract

We present an algorithm that constructs Calabi-Yau threefold orientifolds and their F-theory uplifts to elliptically-fibered Calabi-Yau fourfolds, embedded in toric varieties at codimension one and two respectively. The resulting Calabi-Yau fourfolds arise from triangulations of 6d reflexive polytopes -- which our method constructs from orientifold data -- and are smooth away from isolated terminal singularities. For many of our fourfolds, the construction of the mirror manifold is immediate, enabling the computation of fourfold periods, and thus the seven-brane superpotential. We present multiple examples that demonstrate these capabilities. Our algorithms work with CYTools and are available through a GitHub repository.

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Cite

BibTeXRIS
BibTeX
@misc{hassfeld2026calabiyau,
  title = {{Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts}},
  author = {Bjoern Hassfeld and Jakob Moritz},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.19423},
  eprint = {2606.19423},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.19423},
}
RIS
TY  - UNPB
TI  - Calabi-Yau Orientifold Hypersurfaces and their F-theory Uplifts
AU  - Bjoern Hassfeld
AU  - Jakob Moritz
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2606.19423
UR  - https://arxiv.org/abs/2606.19423
AB  - We present an algorithm that constructs Calabi-Yau threefold orientifolds and their F-theory uplifts to elliptically-fibered Calabi-Yau fourfolds, embedded in toric varieties at codimension one and two respectively. The resulting Calabi-Yau fourfolds arise from triangulations of 6d reflexive polytopes -- which our method constructs from orientifold data -- and are smooth away from isolated terminal singularities. For many of our fourfolds, the construction of the mirror manifold is immediate, enabling the computation of fourfold periods, and thus the seven-brane superpotential. We present multiple examples that demonstrate these capabilities. Our algorithms work with CYTools and are available through a GitHub repository.
ER  -