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PreprintCC BY 4.0arXiv

A quantum connection approach to rationality

  • Luiz Carazolli
  • Leonardo F. Cavenaghi
  • Ludmil Katzarkov
  • Maxim Kontsevich
  • Pedro Antonio Muniz Martins
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Abstract

We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. Applications include showing non-rationality of cubic threefolds, ordinary Gushel--Mukai threefolds, very general quartic fourfolds, and products of the threefolds with PP1.

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Cite

BibTeXRIS
BibTeX
@misc{carazolli2026quantum,
  title = {{A quantum connection approach to rationality}},
  author = {Luiz Carazolli and Leonardo F. Cavenaghi and Ludmil Katzarkov and Maxim Kontsevich and Pedro Antonio Muniz Martins},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.06669},
  eprint = {2610.06669},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.06669},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A quantum connection approach to rationality
AU  - Luiz Carazolli
AU  - Leonardo F. Cavenaghi
AU  - Ludmil Katzarkov
AU  - Maxim Kontsevich
AU  - Pedro Antonio Muniz Martins
PY  - 2026
DA  - 2026/10/05
PB  - arXiv
DO  - 10.48550/arxiv.2610.06669
UR  - https://arxiv.org/abs/2610.06669
AB  - We extract rank and regularized exponents from cyclic generic factors of the quantum connection and show that these data persist under the birational comparisons considered here. Applications include showing non-rationality of cubic threefolds, ordinary Gushel--Mukai threefolds, very general quartic fourfolds, and products of the threefolds with PP^1.
ER  -