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, Delta) with K-X + Delta numerically trivial and not of product type, in dimension at most four.
Birational boundedness of low-dimensional elliptic Calabi-Yau varieties with a section / G. Di Cerbo, R. Svaldi. - In: COMPOSITIO MATHEMATICA. - ISSN 0010-437X. - 157:8(2021 Aug), pp. 1766-1806. [10.1112/S0010437X2100717X]
Birational boundedness of low-dimensional elliptic Calabi-Yau varieties with a section
R. Svaldi
2021
Abstract
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, Delta) with K-X + Delta numerically trivial and not of product type, in dimension at most four.File | Dimensione | Formato | |
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