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K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties
Abstract
Let M=X6σ be a smooth Debarre-Voisin hyperkähler fourfold and X=X3σ the associated smooth hyperplane section of Gr(3,10). Using the incidence correspondence between X and M, we construct a family ℰ of objects in the Kuznetsov component Ku(X). We write v for the common Mukai vector of its fibers. We prove that the associated Mukai homomorphism Θℰ|v⊥: v⊥xrightarrow∼H2(M,ℤ) is an integral Hodge isometry and explicitly determine the inverse image of the Plücker polarization. For a very general point of the trivector divisor corresponding to discriminant $24$, we also construct an integral Hodge isometry between the full Mukai lattices of Ku(X) and the associated twisted K3 surface.
Related
- Ambient Chow Rings of Debarre--Voisin Fourfolds and the Beauville--Voisin Conjecture
- Gushel–Mukai varieties
- Monoidal Categories associated with Kac-Moody Open Richardson Varieties in Symmetric Type
- Fourier-Mukai transforms by a family of stable sheaves and preservation of stability
- Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
BibTeX
@misc{akazawa2026categories,
title = {{K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties}},
author = {Ryo Akazawa},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04602},
eprint = {2611.04602},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04602},
}
RIS
TY - UNPB
TI - K3 Categories and Mukai Homomorphisms for Debarre-Voisin Varieties
AU - Ryo Akazawa
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04602
UR - https://arxiv.org/abs/2611.04602
AB - Let M=X_6^σ be a smooth Debarre-Voisin hyperkähler fourfold and X=X_3^σ the associated smooth hyperplane section of Gr(3,10). Using the incidence correspondence between X and M, we construct a family ℰ of objects in the Kuznetsov component Ku(X). We write v for the common Mukai vector of its fibers. We prove that the associated Mukai homomorphism Θ_ℰ|_v^⊥: v^⊥xrightarrow∼H^2(M,ℤ) is an integral Hodge isometry and explicitly determine the inverse image of the Plücker polarization. For a very general point of the trivector divisor corresponding to discriminant $24$, we also construct an integral Hodge isometry between the full Mukai lattices of Ku(X) and the associated twisted K3 surface.
ER -