On the Fukaya categories of projective hypersurfaces of general type
Kazushi Ueda
TL;DR
This paper proves homological mirror symmetry for high-degree projective hypersurfaces by establishing a functor between wrapped and boundary Fukaya categories, advancing understanding of symplectic geometry and mirror symmetry.
Contribution
It introduces a new functor linking wrapped and boundary Fukaya categories, enabling proof of homological mirror symmetry for certain hypersurfaces.
Findings
Homological mirror symmetry established for high-degree hypersurfaces
Construction of a functor between wrapped and boundary Fukaya categories
Advancement in symplectic geometry techniques
Abstract
We prove homological mirror symmetry for projective hypersurfaces of sufficiently high degree using a functor from the wrapped Fukaya category of an affine hypersurface to the Fukaya category of its boundary at infinity.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Mathematics and Applications