Homological mirror symmetry for the quintic 3-fold
Yuichi Nohara, Kazushi Ueda
TL;DR
This paper proves homological mirror symmetry for the quintic Calabi-Yau 3-fold, extending previous methods and establishing compatibility with projective space, advancing understanding in mirror symmetry for complex geometries.
Contribution
It provides a new proof of homological mirror symmetry for the quintic 3-fold, building on Seidel's approach and ensuring compatibility with projective space.
Findings
Homological mirror symmetry is established for the quintic Calabi-Yau 3-fold.
The proof aligns with Seidel's approach for the quartic surface.
Compatibility with projective space and its Calabi-Yau hypersurface is demonstrated.
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.
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