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

Gabriele Di Cerbo, Roberto Svaldi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

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, Δ) with KX + Δ numerically trivial and not of product type, in dimension at most four.

Original languageEnglish (US)
Pages (from-to)1766-1806
Number of pages41
JournalCompositio Mathematica
Volume157
Issue number8
DOIs
StatePublished - Aug 2021

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Boundedness of algebraic varieties
  • Calabi–Yau varieties
  • Elliptic fibrations
  • Log Calabi–Yau pairs

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