Homological mirror symmetry for Batyrev mirror pairs
Sheel Ganatra, Andrew Hanlon, Jeff Hicks, Daniel Pomerleano, Nick, Sheridan
TL;DR
This paper proves Kontsevich's homological mirror symmetry conjecture for a broad class of Calabi-Yau hypersurfaces in toric varieties, specifically those constructed by Batyrev from dual reflexive polytopes, across various characteristics.
Contribution
It establishes the homological mirror symmetry conjecture for Batyrev mirror pairs of Calabi-Yau hypersurfaces, extending previous results to a large class of examples.
Findings
Proves homological mirror symmetry for Batyrev mirror pairs
Valid in characteristic zero and almost all positive characteristics
Extends the class of Calabi-Yau hypersurfaces satisfying the conjecture
Abstract
We prove Kontsevich's homological mirror symmetry conjecture for a large class of mirror pairs of Calabi--Yau hypersurfaces in toric varieties. These mirror pairs were constructed by Batyrev from dual reflexive polytopes. The theorem holds in characteristic zero and in all but finitely many positive characteristics.
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Taxonomy
TopicsNonlinear Waves and Solitons · Molecular spectroscopy and chirality · Homotopy and Cohomology in Algebraic Topology