Singularities of admissible normal functions (with an appendix by Najmuddin Fakhruddin)

• 成果类型: Article
• 署名作者: Brosnan, Patrick; Fang, Hao; Nie, Zhaohu; Pearlstein, Gregory
• 署名单位: University of British Columbia; University of Iowa; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Michigan State University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0191-9
• 发表日期: 2009
• 页码: 599-629
• 关键词: mixed hodge modules

摘要

In a recent paper, M. Green and P. Griffiths used R. Thomas' work on nodal hypersurfaces to sketch a proof of the equivalence of the Hodge conjecture and the existence of certain singular admissible normal functions. Inspired by their work, we study normal functions using Morihiko Saito's mixed Hodge modules and prove that the existence of singularities of the type considered by Griffiths and Green is equivalent to the Hodge conjecture. Several of the intermediate results, including a relative version of the weak Lefschetz theorem for perverse sheaves, are of independent interest.