Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 1 h ago
Peer-reviewedCC BYAlgebraic geometry

Calabi–Yau varieties of large index

  • Louis Esser
  • Burt Totaro
  • Chengxi Wang
Open at sourcePDFDOICite

Abstract

Call a projective variety X Calabi-Yau if its canonical divisor is Q-linearly equivalent to zero.The smallest positive integer m with mK X linearly equivalent to zero is called the index of X.We construct Calabi-Yau varieties with the largest known index in high dimensions.In our examples, the index grows doubly exponentially with dimension.We conjecture that our examples have the largest possible index, with supporting evidence in low dimensions.The examples are obtained by mirror symmetry from our Calabi-Yau varieties with an ample Weil divisor of small volume.We also give examples for several related problems, including Calabi-Yau varieties with large orbifold Betti numbers or small minimal log discrepancy.

Related

  1. On the Witt liftability of quasi-F-split Calabi--Yau varieties
    Teppei Takamatsu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. Characterising canonical lifts of ordinary Calabi-Yau varieties
    Samuel A. Moore
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv
  3. Meromorphic modular differential equations for the elliptic genus of Calabi--Yau varieties
    Dmitrii Adler, Valery Gritsenko
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Hybrid toric varieties and the non-archimedean SYZ fibration on Calabi–Yau hypersurfaces
    Léonard Pille-Schneider
    Algebraic geometryPeer-reviewedCC BYFull text16 citedGeometry & topologyOpenAlex
  5. On polarizations of affine Calabi--Yau varieties
    Yueqiao Wu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@article{esser2026calabiyau,
  title = {{Calabi–Yau varieties of large index}},
  author = {Louis Esser and Burt Totaro and Chengxi Wang},
  journal = {Algebraic geometry},
  year = {2026},
  month = aug,
  doi = {10.14231/ag-2026-019},
  url = {https://doi.org/10.14231/ag-2026-019},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - Calabi–Yau varieties of large index
AU  - Louis Esser
AU  - Burt Totaro
AU  - Chengxi Wang
PY  - 2026
DA  - 2026/08/21
JO  - Algebraic geometry
DO  - 10.14231/ag-2026-019
UR  - https://doi.org/10.14231/ag-2026-019
AB  - Call a projective variety X Calabi-Yau if its canonical divisor is Q-linearly equivalent to zero.The smallest positive integer m with mK X linearly equivalent to zero is called the index of X.We construct Calabi-Yau varieties with the largest known index in high dimensions.In our examples, the index grows doubly exponentially with dimension.We conjecture that our examples have the largest possible index, with supporting evidence in low dimensions.The examples are obtained by mirror symmetry from our Calabi-Yau varieties with an ample Weil divisor of small volume.We also give examples for several related problems, including Calabi-Yau varieties with large orbifold Betti numbers or small minimal log discrepancy.
SN  - 2214-2584
SN  - 2313-1691
ER  -