Degenerated Calabi–Yau varieties with infinite components, moduli compactifications, and limit toroidal structures

For any degenerating Calabi–Yau family, we introduce a new limit space which call galaxy, whose dense subspace is the disjoint union of countably infinite open varieties, parametrized by rational points Kontsevich–Soibelman’s essential skeleton, while dominated Huber adification over Puiseux series field. Other topics include: projective limits toroidal compactifications (Sect. 3), locally modelled on toric varieties 2.4), way to attach tropicalized family given 4), are weakly related each other.