Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 56 min ago
PreprintCC0arXiv

The Verra involution on special cubic fourfolds

  • Augustinas Jacovskis
  • Reinder Meinsma
  • Riccardo Moschetti
Open at sourcePDFDOICite

Abstract

We present a detailed study of the Hodge theory, geometry and derived categories of Verra fourfolds, and their relationship with twisted K3 surfaces and cubic fourfolds. We classify Brauer classes of Verra type on K3 surfaces of degree 2, and use this to derive an explicit counting formula for Fourier--Mukai partners of a large class of Verra fourfolds. We develop the basic theory of cohomology of Verra fourfolds and apply it to prove a derived Torelli theorem for a large class of Verra fourfolds. As an application, we prove that L-equivalent Verra fourfolds in this class are Fourier--Mukai partners, and conjecture that this implication holds for all Verra fourfolds. We then give a construction of cubic fourfolds birational to Verra fourfolds. The construction yields examples of cubic and Verra fourfolds whose associated twisted K3 surfaces have non-trivial Brauer classes. Therefore, these fourfolds are expected to be irrational.

Related

  1. Classification of Automorphism Groups of Smooth Cubic Threefolds and Fourfolds
    Jie Fu, Shihao Wang, Zhiwei Zheng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  2. On the Supersingular reduction of Cubic fourfolds with Complex Multiplication
    Temma Yamagishi
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  3. Derived Torelli for Kuznetsov components of cubic fourfolds
    Hanfei Guo, Ruxuan Zhang
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  4. Remarks on Lattice Actions Corresponding to Automorphism Groups of Smooth Cubic Fourfolds
    Jie Fu
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv
  5. Automorphism Groups of Smooth Cubic Fourfolds through Lattice Theory
    Jie Fu, Zhiwei Zheng
    arXivPreprintarXiv licenceFull textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{jacovskis2026verra,
  title = {{The Verra involution on special cubic fourfolds}},
  author = {Augustinas Jacovskis and Reinder Meinsma and Riccardo Moschetti},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.32952},
  eprint = {2610.32952},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.32952},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - The Verra involution on special cubic fourfolds
AU  - Augustinas Jacovskis
AU  - Reinder Meinsma
AU  - Riccardo Moschetti
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2610.32952
UR  - https://arxiv.org/abs/2610.32952
AB  - We present a detailed study of the Hodge theory, geometry and derived categories of Verra fourfolds, and their relationship with twisted K3 surfaces and cubic fourfolds. We classify Brauer classes of Verra type on K3 surfaces of degree 2, and use this to derive an explicit counting formula for Fourier--Mukai partners of a large class of Verra fourfolds. We develop the basic theory of cohomology of Verra fourfolds and apply it to prove a derived Torelli theorem for a large class of Verra fourfolds. As an application, we prove that L-equivalent Verra fourfolds in this class are Fourier--Mukai partners, and conjecture that this implication holds for all Verra fourfolds. We then give a construction of cubic fourfolds birational to Verra fourfolds. The construction yields examples of cubic and Verra fourfolds whose associated twisted K3 surfaces have non-trivial Brauer classes. Therefore, these fourfolds are expected to be irrational.
ER  -