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On the Supersingular reduction of Cubic fourfolds with Complex Multiplication
Abstract
If X is a K3 surface with complex multiplication by a CM field E, Kazuhiro Ito proved that the height of the reduction of X in characteristic p>0, and its Artin invariant if it is supersingular, can be computed from the decomposition of p in E. We present analogous results for cubic fourfolds by using the main theorem of complex multiplication for cubic fourfold, proved by Rikuto Ito.
Related
- Legendre polynomials and complex multiplication, II: class numbers of quadratic fields and genus 2 supersingular polynomials
- Bad Reduction of Genus Two Curves with complex multiplication
- Classification of Automorphism Groups of Smooth Cubic Threefolds and Fourfolds
- Derived Torelli for Kuznetsov components of cubic fourfolds
- Remarks on Lattice Actions Corresponding to Automorphism Groups of Smooth Cubic Fourfolds
BibTeX
@misc{yamagishi2026supersingular,
title = {{On the Supersingular reduction of Cubic fourfolds with Complex Multiplication}},
author = {Temma Yamagishi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.38498},
eprint = {2610.38498},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.38498},
}
RIS
TY - UNPB
TI - On the Supersingular reduction of Cubic fourfolds with Complex Multiplication
AU - Temma Yamagishi
PY - 2026
DA - 2026/10/28
PB - arXiv
DO - 10.48550/arxiv.2610.38498
UR - https://arxiv.org/abs/2610.38498
AB - If X is a K3 surface with complex multiplication by a CM field E, Kazuhiro Ito proved that the height of the reduction of X in characteristic p>0, and its Artin invariant if it is supersingular, can be computed from the decomposition of p in E. We present analogous results for cubic fourfolds by using the main theorem of complex multiplication for cubic fourfold, proved by Rikuto Ito.
ER -