Identifying exceptional–quantum decomposition factors

Identify each factor Am appearing in the decomposition of QH*(X)|q near an extremal-contraction boundary of the Kähler moduli space with the (big) quantum cohomology of a naturally associated space.

Background

When the quantum parameter approaches a boundary corresponding to an extremal contraction, the small quantum product specializes to an f-exceptional product and QH*(X)|q decomposes into factors indexed by points of a limiting spectrum. Several examples suggest these factors match quantum cohomology of birational models or loci (e.g., base, flips, or exceptional centers), but a general identification remains to be established.