PreprintCC BY-NC-ND 4.0arXiv
Geometric realizations of Brauer classes on K3 surfaces from hyperkähler contractions
Abstract
Elements of the Brauer group Br(S) of a variety S have geometric incarnations as étale-projective S-bundles, yet producing minimalist constructions of such bundles, which often power arithmetic applications, remains a difficult problem. When S is a K3 surface with Picard rank $1$, we use the birational geometry of moduli spaces of twisted sheaves on S to construct geometric realizations of nontrivial elements of Br(S). We recover many known geometric constructions of Brauer classes on K3 surfaces while providing a common moduli-theoretic framework for them. As a by-product, we give a new proof of the period-index theorem for very general K3 surfaces.
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BibTeX
@misc{frei2026geometric,
title = {{Geometric realizations of Brauer classes on K3 surfaces from hyperkähler contractions}},
author = {Sarah Frei and Jack Petok and Anthony Várilly-Alvarado},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.15892},
eprint = {2609.15892},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.15892},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Geometric realizations of Brauer classes on K3 surfaces from hyperkähler contractions
AU - Sarah Frei
AU - Jack Petok
AU - Anthony Várilly-Alvarado
PY - 2026
DA - 2026/09/14
PB - arXiv
DO - 10.48550/arxiv.2609.15892
UR - https://arxiv.org/abs/2609.15892
AB - Elements of the Brauer group Br(S) of a variety S have geometric incarnations as étale-projective S-bundles, yet producing minimalist constructions of such bundles, which often power arithmetic applications, remains a difficult problem. When S is a K3 surface with Picard rank $1$, we use the birational geometry of moduli spaces of twisted sheaves on S to construct geometric realizations of nontrivial elements of Br(S). We recover many known geometric constructions of Brauer classes on K3 surfaces while providing a common moduli-theoretic framework for them. As a by-product, we give a new proof of the period-index theorem for very general K3 surfaces.
ER -