Periods of fibre products of elliptic surfaces and the Gamma conjecture

2025/05/12 by Eric Pichon-Pharabod, Pichon-Pharabod, Eric
Mathematics · #14J32 #14J33 (Secondary) #14Q15 #32G20 (Primary) 14D05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Computer and information sciences #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2505.07685

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We provide an algorithm for computing a basis of homology of fibre products of elliptic surfaces over \mathbb P¹, along with the corresponding intersection product and period matrices. We use this data to investigate the Gamma conjecture for Calabi-Yau threefolds obtained in this manner. We find a formula that works for all operators of a list of 105 fibre products, as well as for fourth order operators of the Calabi-Yau database. This algorithm comes with a SageMath implementation.

Citations

• Numerical Calculation of Periods on Schoen's Class of Calabi-Yau Threefolds
• In search of almost generic Calabi-Yau 3-folds
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Hadamard products and BPS networks
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• Calabi-Yau operators of degree two
• The Donaldson-Thomas partition function of the banana manifold
• Real and complex multiplication on K3 surfaces via period integration
• Computing period matrices and the Abel-Jacobi map of superelliptic\n curves
• Calabi--Yau Operators
• Ore Polynomials in Sage
• NumGfun: a Package for Numerical and Analytic Computation with D-finite Functions
• Elliptic Surfaces
• Hodge theoretic aspects of mirror symmetry
• Fiber products of elliptic surfaces with section and associated Kummer fibrations
• Tables of Calabi--Yau equations
• Factoring polynomials with rational coefficients

Related

• Some Identities For Periods of Hulek-Verrill Threefolds
• Numerical Calculation of Periods on Schoen's Class of Calabi-Yau Threefolds
• Product-Quotient Surfaces: new invariants and algorithms
• Correspondences between modular Calabi--Yau fiber products
• Periods of CY n-folds and mixed Tate motives, a numerical study