Derived Categories of BHK Mirrors
David Favero, Tyler L. Kelly
TL;DR
This paper establishes a derived category equivalence for BHK mirror pairs and proves Homological Mirror Symmetry for certain mirror pencils, advancing the understanding of mirror symmetry in algebraic geometry.
Contribution
It provides the first derived category analogue of BHK mirror birationality and proves Homological Mirror Symmetry for BHK mirror pencils in projective space.
Findings
Derived categories of BHK mirrors are equivalent.
Homological Mirror Symmetry holds for BHK mirror pencils.
New techniques connect birationality and homological properties in mirror symmetry.
Abstract
We prove a derived analogue to the results of Borisov, Clarke, Kelly, and Shoemaker on the birationality of Berglund-Hubsch-Krawitz mirrors. Heavily bootstrapping off work of Seidel and Sheridan, we obtain Homological Mirror Symmetry for Berglund-Hubsch-Krawitz mirror pencils to hypersurfaces in projective space.
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