3 papers
math.AG2025
King's Conjecture and the Cox category
Matthew R. Ballard, Christine Berkesch, Michael K. Brown +6
We state and prove a realization of King's Conjecture for a category glued from the derived categories of all of the toric varieties arising from a given Cox ring. Our perspective…
math.AG2025
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…
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…