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PreprintarXiv licencearXiv

Derived Torelli for Kuznetsov components of cubic fourfolds

  • Hanfei Guo
  • Ruxuan Zhang
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Abstract

We prove that every orientation-preserving Hodge isometry between the integral Mukai lattices of the Kuznetsov components of two smooth cubic fourfolds is induced by an exact equivalence. The proof uses Markman--Mehrotra's comonad reconstruction method to recover both Kuznetsov components from a common Fourier--Mukai comonad on a moduli space of stable objects. As an application, we prove that the Kuznetsov components of two smooth cubic fourfolds are equivalent whenever their Fano varieties of lines are derived equivalent.

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Cite

BibTeXRIS
BibTeX
@misc{guo2026derived,
  title = {{Derived Torelli for Kuznetsov components of cubic fourfolds}},
  author = {Hanfei Guo and Ruxuan Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01716},
  eprint = {2611.01716},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01716},
}
RIS
TY  - UNPB
TI  - Derived Torelli for Kuznetsov components of cubic fourfolds
AU  - Hanfei Guo
AU  - Ruxuan Zhang
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01716
UR  - https://arxiv.org/abs/2611.01716
AB  - We prove that every orientation-preserving Hodge isometry between the integral Mukai lattices of the Kuznetsov components of two smooth cubic fourfolds is induced by an exact equivalence. The proof uses Markman--Mehrotra's comonad reconstruction method to recover both Kuznetsov components from a common Fourier--Mukai comonad on a moduli space of stable objects. As an application, we prove that the Kuznetsov components of two smooth cubic fourfolds are equivalent whenever their Fano varieties of lines are derived equivalent.
ER  -