A decomposition theorem for singular spaces with trivial canonical class of dimension at most five

• 成果类型: Article
• 署名作者: Druel, Stephane
• 署名单位: Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS)
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-017-0748-y
• 发表日期: 2018
• 页码: 245-296
• 关键词: 1st chern class; vector-bundles; minimal models; kodaira dimension; general type; VARIETIES; foliations; Manifold; sheaves; FIELDS

摘要

In this paper we partly extend the Beauville-Bogomolov decomposition theorem to the singular setting. We show that any complex projective variety of dimension at most five with canonical singularities and numerically trivial canonical class admits a finite cover, ,tale in codimension one, that decomposes as a product of an Abelian variety, and singular analogues of irreducible Calabi-Yau and irreducible holomorphic symplectic varieties.