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Peer-reviewedCC BYAlgebraic geometry

Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces

  • Léonard Pille-Schneider1,2,3
  1. 1Algèbre et Géométrie (DMA)
  2. 2Centre de Mathématiques Laurent Schwartz
  3. 3Département de Mathématiques et Applications - ENS Paris
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Abstract

Using a construction by Yamamoto of contraction maps from tropical Calabi-Yau varieties to their dual intersection complex, we construct a non-archimedean SYZ fibration for a class of maximally degenerate hypersurfaces in projective space.We furthermore prove that under a discrete symmetry assumption, the potential for the nonarchimedean Calabi-Yau metric is constant along the fibers of the retraction.The proof uses the work of Li on the Fermat degeneration of hypersurfaces, and an explicit description of toric plurisubharmonic metrics on the hybrid space associated with a complex toric variety.

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Cite

BibTeXRIS
BibTeX
@article{pilleschneider2026hybrid,
  title = {{Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces}},
  author = {Léonard Pille-Schneider},
  journal = {Algebraic geometry},
  year = {2026},
  month = jun,
  doi = {10.14231/ag-2026-016},
  url = {https://doi.org/10.14231/ag-2026-016},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces
AU  - Léonard Pille-Schneider
PY  - 2026
DA  - 2026/06/12
JO  - Algebraic geometry
DO  - 10.14231/ag-2026-016
UR  - https://doi.org/10.14231/ag-2026-016
AB  - Using a construction by Yamamoto of contraction maps from tropical Calabi-Yau varieties to their dual intersection complex, we construct a non-archimedean SYZ fibration for a class of maximally degenerate hypersurfaces in projective space.We furthermore prove that under a discrete symmetry assumption, the potential for the nonarchimedean Calabi-Yau metric is constant along the fibers of the retraction.The proof uses the work of Li on the Fermat degeneration of hypersurfaces, and an explicit description of toric plurisubharmonic metrics on the hybrid space associated with a complex toric variety.
SN  - 2214-2584
SN  - 2313-1691
ER  -