Viehweg's hyperbolicity conjecture for families with maximal variation

• 成果类型: Article
• 署名作者: Popa, Mihnea; Schnell, Christian
• 署名单位: Northwestern University; State University of New York (SUNY) System; Stony Brook University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0698-9
• 发表日期: 2017
• 页码: 677-713
• 关键词: canonically polarized varieties; Positivity; STABILITY

摘要

We use the theory of Hodge modules to construct Viehweg-Zuo sheaves on base spaces of families with maximal variation and fibers of general type and, more generally, families whose geometric generic fiber has a good minimal model. Combining this with a result of Campana-Pun, we deduce Viehweg's hyperbolicity conjecture in this context, namely the fact that the base spaces of such families are of log general type. This is approached as part of a general problem of identifying what spaces can support Hodge theoretic objects with certain positivity properties.