A Finiteness Theorem for Elliptic Calabi-Yau Threefolds

1993/05/03 by Mark Gross, Gross, M. · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9305002

openalex publication_date 1993/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that up to birational equivalence, there exists only a finite number of families of Calabi-Yau threefolds (i.e. a threefold with trivial canonical class and factorial terminal singularities) which have an elliptic fibration to a rational surface. This strengthens a result of B. Hunt that there are only a finite number of possible Euler characteristics for such threefolds.

Cited by

• Statistics of Base Polytopes in F-theory
• Explicit Bounds on the Spectrum of 6d N=(1,0) Supergravity
• A Picard rank bound for base surfaces of elliptic Calabi-Yau 3-folds

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