Tables of Calabi--Yau equations

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.

130 pages

References in corpus (5)

• Considerations of One-Modulus Calabi-Yau Compactifications: Picard-Fuchs Equations, Kähler Potentials and Mirror Maps
• Differential equations, mirror maps and zeta values
• Mirror Maps and Instanton Sums for Complete Intersections in Weighted Projective Space
• Lines on Calabi Yau complete intersections, mirror symmetry, and Picard Fuchs equations
• Sums of squares of binomial coefficients, with applications to Picard-Fuchs equations

Cited by in corpus (49)

• Computing periods of rational integrals
• Moduli-dependent Species Scale
• Arithmeticity of Certain Symplectic Hypergeometric Groups
• Differential equations, mirror maps and zeta values
• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions
• The Ising model: from elliptic curves to modular forms and Calabi-Yau equations
• Quantum periods of Calabi-Yau fourfolds
• Bounds for smooth Fano weighted complete intersections
• Supercongruences for rigid hypergeometric Calabi--Yau threefolds
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• Monodromy calculatons of fourth order equations of Calabi-Yau type
• Open mirror symmetry for Pfaffian Calabi-Yau 3-folds
• Arithmeticity of Four Hypergeometric Monodromy Groups associated to Calabi-Yau threefolds
• Some monodromy groups of finite index in $S{p}_4(\mathbb{Z})$
• Time reversal and $\mathbf{CP}$ invariance in Calabi-Yau compactifications
• Finiteness and the Emergence of Dualities
• Multivariate $p$-adic formal congruences and integrality of Taylor coefficients of mirror maps
• Deligne's conjecture and mirror symmetry
• Criterion for the integrality of the Taylor coefficients of mirror maps in several variables
• A Note on Computations of D-brane Superpotential
• The Geometry of Gauged Linear Sigma Model Correlation Functions
• GLSMs, joins, and nonperturbatively-realized geometries
• Topological Strings on Non-Commutative Resolutions
• Ising n-fold integrals as diagonals of rational functions and integrality of series expansions: integrality versus modularity
• Analytic Periods via Twisted Symmetric Squares
• Dwork Congruences and reflexive Polytopes
• Sequences, modular forms and cellular integrals
• Minuscule Schubert Varieties and Mirror Symmetry
• Monodromy of Picard-Fuchs differential equations for Calabi-Yau threefolds
• Hodge classes associated to 1-parameter families of Calabi-Yau 3-folds
• On Dwork's p-adic formal congruences theorem and hypergeometric mirror maps
• On the Quantum K-Theory of the Quintic
• The art of finding Calabi-Yau differential eq1uations
• Determinantal Quintics and Mirror Symmetry of Reye Congruences
• On $p$-integrality of instanton numbers
• Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
• Classical Weight-Four L-value Ratios as Sums of Calabi--Yau Invariants
• Two One-Parameter Special Geometries
• Schwarzian conditions for linear differential operators with selected differential Galois groups (unabridged version)
• Transformations of Jesus Guillera's formulas for 1/Pi^2
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Fano-Mathieu correspondence
• B-type D-branes in hybrid models
• Local Zeta Functions From Calabi-Yau Differential Equations
• Mirror Symmetry of Minimal Calabi-Yau Manifolds
• Differential algebra on lattice Green functions and Calabi-Yau operators (unabridged version)
• Modular-type functions attached to Calabi-Yau varieties: integrality properties
• Diagonals of rational functions: from differential algebra to effective algebraic geometry (unabridged version)
• Orthogonal Hypergeometric Groups with a Maximally Unipotent Monodromy