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- Title
Birational boundedness of low-dimensional elliptic Calabi–Yau varieties with a section.
- Authors
Di Cerbo, Gabriele; Svaldi, Roberto
- Abstract
We prove that there are finitely many families, up to isomorphism in codimension one, of elliptic Calabi–Yau manifolds $Y\rightarrow X$ with a rational section, provided that $\dim (Y)\leq 5$ 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 $(X, \Delta)$ with $K_X+\Delta$ numerically trivial and not of product type, in dimension at most four.
- Subjects
CALABI-Yau manifolds; ALGEBRAIC varieties
- Publication
Compositio Mathematica, 2021, Vol 157, Issue 8, p1766
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X2100717X