Year: 2026
Type: preprint
Abstract: Elements of the Brauer group $\operatorname{Br}(S)$ 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 $\operatorname{Br}(S)$. 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.
Source: arXiv (Cornell University)
Institution: Colby College
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213335361