Birationally rigid hypersurfaces

• 成果类型: Article
• 署名作者: de Fernex, Tommaso
• 署名单位: Utah System of Higher Education; University of Utah
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-012-0417-0
• 发表日期: 2013
• 页码: 533-566
• 关键词: log discrepancies; jet schemes; SINGULARITIES; AUTOMORPHISMS; inversion

摘要

We prove that for Na parts per thousand yen4, all smooth hypersurfaces of degree N in a(TM) (N) are birationally superrigid. First discovered in the case N=4 by Iskovskikh and Manin in a work that started this whole direction of research, this property was later conjectured to hold in general by Pukhlikov. The proof relies on the method of maximal singularities in combination with a formula on restrictions of multiplier ideals.