发表机构
Rice University; Colby College（莱斯大学; 科尔比学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过扭曲层模空间的双有理几何，为Picard秩1的K3曲面上的Brauer类构造几何实现，统一了已知构造并新证周期-指数定理。
AI 中文摘要
簇$S$的Brauer群$\operatorname{Br}(S)$中的元素具有作为étale-射影$S$-丛的几何体现，然而构造此类丛的最小化构造（这通常为算术应用提供动力）仍然是一个困难的问题。当$S$是Picard秩为1的K3曲面时，我们利用$S$上扭曲层的模空间的双有理几何来构造$\operatorname{Br}(S)$中非平凡元素的几何实现。我们恢复了K3曲面上Brauer类的许多已知几何构造，同时为它们提供了一个共同的模理论框架。作为副产品，我们给出了非常一般的K3曲面的周期-指数定理的新证明。
英文摘要
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.
Comments56 pages, 2 figures, 9 tables
