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

Gabriele Di Cerbo; Roberto Svaldi

doi:10.1112/S0010437X2100717X

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

Gabriele Di Cerbo
, Roberto Svaldi

Mathematics

Research output: Contribution to journal › Article › peer-review

35 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 K_X + Δ numerically trivial and not of product type, in dimension at most four.

Original language	English (US)
Pages (from-to)	1766-1806
Number of pages	41
Journal	Compositio Mathematica
Volume	157
Issue number	8
DOIs	https://doi.org/10.1112/S0010437X2100717X
State	Published - 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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10.1112/S0010437X2100717X

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title = "Birational boundedness of low-dimensional elliptic Calabi–Yau varieties with a section",

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.",

keywords = "Boundedness of algebraic varieties, Calabi–Yau varieties, Elliptic fibrations, Log Calabi–Yau pairs",

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year = "2021",

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doi = "10.1112/S0010437X2100717X",

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T1 - Birational boundedness of low-dimensional elliptic Calabi–Yau varieties with a section

AU - Di Cerbo, Gabriele

AU - Svaldi, Roberto

PY - 2021/8

Y1 - 2021/8

N2 - 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.

AB - 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.

KW - Boundedness of algebraic varieties

KW - Calabi–Yau varieties

KW - Elliptic fibrations

KW - Log Calabi–Yau pairs

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UR - https://www.scopus.com/pages/publications/85114229890#tab=citedBy

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VL - 157

SP - 1766

EP - 1806

JO - Compositio Mathematica

JF - Compositio Mathematica

IS - 8

ER -

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

Abstract

All Science Journal Classification (ASJC) codes

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