We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi–Yau manifolds Y → X with a rational section, provided that dim(Y) ≤ 5 and Y is not of product type. As a consequence, we obtain that there are finitely many possibilities for the Hodge diamond of such manifolds. The result follows from log birational boundedness of Kawamata log terminal pairs (X, Δ) with KX + Δ numerically trivial and not of product type, in dimension at most four.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Boundedness of algebraic varieties
- Calabi–Yau varieties
- Elliptic fibrations
- Log Calabi–Yau pairs