3 papers
math.SG2026
Monodromy action of mirror stops for toric Calabi-Yau surfaces
Michela Barbieri, Andrew Hanlon, Jeff Hicks
Mirror symmetry predicts an action by the fundamental group of a conjectural stringy Kähler moduli space on the derived category of an algebraic variety. For a toric variety, a mod…
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.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…