4 papers
On the positivity and integrality of coefficients of mirror maps
Sophie Bleau, Nick Sheridan
We present natural conjectural generalizations of the `positivity and integrality of mirror maps' phenomenon, encompassing the mirror maps appearing in the Batyrev--Borisov constru…
The cyclic open--closed map and variations of Hodge structures
Sheel Ganatra, Nick Sheridan
We construct the cyclic open--closed map for the big (i.e., bulk-deformed) relative Fukaya category, in the semipositive case, and show that it is a morphism of `polarized variatio…
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…
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…