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Ambient Chow Rings of Debarre--Voisin Fourfolds and the Beauville--Voisin Conjecture
Abstract
We prove the Beauville--Voisin conjecture for a very general Debarre--Voisin hyperkähler fourfold Y⊂Gr(6,10) associated with a trivector σ on a ten-dimensional complex vector space V10. Namely, the cycle class map is injective on the subalgebra of the Chow ring generated by divisor classes and the Chern classes of the tangent bundle.
Related
- K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties
- The Tate conjecture for powers of abelian fourfolds and the Hodge conjecture for powers of CM fourfolds
- The Tate conjecture for abelian fourfolds over finite fields
- The Hodge conjecture for Fermat fourfolds of degree at most 100, and the semi-standard obstruction at degree 70
- Irrational families of Fano weighted complete intersection fourfolds
BibTeX
@misc{akazawa2026ambient,
title = {{Ambient Chow Rings of Debarre--Voisin Fourfolds and the Beauville--Voisin Conjecture}},
author = {Ryo Akazawa},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23376},
eprint = {2610.23376},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23376},
}
RIS
TY - UNPB
TI - Ambient Chow Rings of Debarre--Voisin Fourfolds and the Beauville--Voisin Conjecture
AU - Ryo Akazawa
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23376
UR - https://arxiv.org/abs/2610.23376
AB - We prove the Beauville--Voisin conjecture for a very general Debarre--Voisin hyperkähler fourfold Y⊂Gr(6,10) associated with a trivector σ on a ten-dimensional complex vector space V_10. Namely, the cycle class map is injective on the subalgebra of the Chow ring generated by divisor classes and the Chern classes of the tangent bundle.
ER -