PreprintCC BY-SA 4.0arXiv
Notes on the Kuznetsov component of cubic sevenfolds
Abstract
Let Y be a cubic 7-fold. When Y is smooth, its Kuznetsov component is a Calabi-Yau category of dimension 3, and we construct an embedding of the Kuznetsov component into the derived category of Clifford modules over ℙ4. When Y is a general cubic 7-fold singular along a line, we construct an explicit weakly crepant categorical resolution of its Kuznetsov component by the derived category of a smooth Calabi-Yau 3-fold, recovering a result of Favero-Kelly. In this construction, we express the resolution functor explicitly as a composition of geometric functors and mutations, and identify its kernel with a category equivalent to a pull-back of the derived category of a stacky curve.
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BibTeX
@misc{liu2026notes,
title = {{Notes on the Kuznetsov component of cubic sevenfolds}},
author = {Peize Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2607.28784},
eprint = {2607.28784},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.28784},
note = {CC BY-SA 4.0},
}
RIS
TY - UNPB
TI - Notes on the Kuznetsov component of cubic sevenfolds
AU - Peize Liu
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2607.28784
UR - https://arxiv.org/abs/2607.28784
AB - Let Y be a cubic 7-fold. When Y is smooth, its Kuznetsov component is a Calabi-Yau category of dimension 3, and we construct an embedding of the Kuznetsov component into the derived category of Clifford modules over ℙ^4. When Y is a general cubic 7-fold singular along a line, we construct an explicit weakly crepant categorical resolution of its Kuznetsov component by the derived category of a smooth Calabi-Yau 3-fold, recovering a result of Favero-Kelly. In this construction, we express the resolution functor explicitly as a composition of geometric functors and mutations, and identify its kernel with a category equivalent to a pull-back of the derived category of a stacky curve.
ER -