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arXiv · 1608.02997

Birational boundedness of low dimensional elliptic Calabi-Yau varieties with a section

Gabriele Di Cerbo·Roberto Svaldi
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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 klt pairs $(X, \Delta)$ with $K_X+\Delta$ numerically trivial and not of product-type, in dimension at most $4$.

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Gabriele Di Cerbo, Roberto Svaldi. 2016-08-09. Birational boundedness of low dimensional elliptic Calabi-Yau varieties with a section. https://doi.org/10.1112/s0010437x2100717x

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