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math.SG2025
Constructing the big relative Fukaya category, and its open--closed maps
Nick Sheridan
This paper continues previous work of the author with Perutz, in which the `small' version of Seidel's relative Fukaya category of a smooth complex projective variety relative to a…
math.SG2024
Homological mirror symmetry for Batyrev mirror pairs
Sheel Ganatra, Andrew Hanlon, Jeff Hicks +2
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…
math.SG2023
Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors
Sheel Ganatra, Andrew Hanlon, Jeff Hicks +2
We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirro…