Tables of Calabi--Yau equations

2005/07/21 by Gert Almkvist, Almkvist, Gert, Christian van Enckevort +5 · 9 citations
Mathematics · Physics and Astronomy · #32S40 #33C20 #34M15 #34M25 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Nonlinear Waves and Solitons #Number Theory (math.NT) #Primary 14J32 #Secondary 11B83

paper · pdf · doi:10.48550/arxiv.math/0507430

openalex publication_date 2005/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main part of this paper is a big table containing what we believe to be a complete list of all fourth order equations of Calabi--Yau type known so far. In the text preceding the tables we explain what a differential equation of Calabi--Yau type is and we briefly discuss how we found these equations. We also describe an electronic version of this list.

Citations

• Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations

Cited by

• Some Identities For Periods of Hulek-Verrill Threefolds
• Fano-Mathieu correspondence
• Mirror Symmetry of Minimal Calabi-Yau Manifolds
• Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds
• On the construction of Calabi-Yau operators
• Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• Modular-type functions attached to Calabi-Yau varieties: integrality\n properties
• Two One-Parameter Special Geometries

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• The art of finding Calabi-Yau differential eq1uations
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• 5-th order differential equations related to Calabi-Yau differential equations
• Calabi-Yau operators of degree two