o-minimal GAGA and a conjecture of Griffiths

• 成果类型: Article
• 署名作者: Bakker, Benjamin; Brunebarbe, Yohan; Tsimerman, Jacob
• 署名单位: University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Bordeaux; University of Toronto
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01166-1
• 发表日期: 2023
• 页码: 163-228
• 关键词: quotients; geometry; domains; MODULI

摘要

We prove a conjecture of Griffiths on the quasi-projectivity of images of period maps using algebraization results arising from o-minimal geometry. Specifically, we first develop a theory of analytic spaces and coherent sheaves that are definable with respect to a given o-minimal structure, and prove a GAGA-type theorem algebraizing definable coherent sheaves on complex algebraic spaces. We then combine this with algebraization theorems of Artin to show that proper definable images of complex algebraic spaces are algebraic. Applying this to period maps, we conclude that the images of period maps are quasi-projective and that the restriction of the Griffiths bundle is ample.