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arXiv · 1111.0632

Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space

Nicholas Sheridan
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Abstract

We prove Homological Mirror Symmetry for a smooth d-dimensional Calabi-Yau hypersurface in projective space, for any d > 2 (for example, d = 3 is the quintic three-fold). The main techniques involved in the proof are: the construction of an immersed Lagrangian sphere in the `d-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.

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Nicholas Sheridan. 2014-01-13. Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space. https://doi.org/10.1007/s00222-014-0507-2

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