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), 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.
Calabi-Yau varieties; log Calabi-Yau pairs; boundedness of algebraic varieties; elliptic fibrations
Settore MAT/03 - Geometria
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/2434/937283
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