Abstract
We describe explicit relations in the symplectomorphism groups of hypersurfaces in toric stacks. To define the elements involved, we construct a proper stack of these hypersurfaces whose boundary represents stable pair degenerations. Our relations arise through the study of the one-dimensional strata of this stack. The results are then examined from the perspective of homological mirror symmetry where we view sequences of relations as maximal degenerations of Landau–Ginzburg models. We then study the $B$-model mirror to these degenerations, which gives a new mirror symmetry approach to the minimal model program.
