Homological mirror symmetry for Calabi-Yau hypersurfaces in projective space

• 成果类型: Article
• 署名作者: Sheridan, Nick
• 署名单位: Princeton University; Institute for Advanced Study - USA
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-014-0507-2
• 发表日期: 2015
• 页码: 1-186
• 关键词: transversality; COHOMOLOGY; CATEGORIES; MANIFOLDS; pairs

摘要

We prove Homological Mirror Symmetry for a smooth -dimensional Calabi-Yau hypersurface in projective space, for any (for example, is the quintic threefold). The main techniques involved in the proof are: the construction of an immersed Lagrangian sphere in the '-dimensional pair of pants'; the introduction of the 'relative Fukaya category', and an understanding of its grading structure; a description of the behaviour of this category with respect to branched covers (via an 'orbifold' Fukaya category); a Morse-Bott model for the relative Fukaya category that allows one to make explicit computations; and the introduction of certain graded categories of matrix factorizations mirror to the relative Fukaya category.