Homological mirror symmetry for the quintic 3-fold

Abstract

We prove homological mirror symmetry for the quintic Calabi-Yau 3-fold. The proof follows that for the quartic surface by Seidel (arXiv:math/0310414) closely, and uses a result of Sheridan (arXiv:1012.3238). In contrast to Sheridan's approach (arXiv:1111.0632), our proof gives the compatibility of homological mirror symmetry for the projective space and its Calabi-Yau hypersurface.

29 pages, 6 figures. v2: revised following the suggestions of the referees

References in corpus (2)

• Homological Mirror Symmetry for Calabi-Yau hypersurfaces in projective space
• Tropical coamoeba and torus-equivariant homological mirror symmetry for the projective space

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• Homology supported in Lagrangian submanifolds in mirror quintic threefolds
• Homological mirror symmetry for local Calabi-Yau manifolds via SYZ
• Quintic periods and stability conditions via homological mirror symmetry