Heun equations coming from geometry

2009/02/04 by Hossein Movasati, Movasati, Hossein, Stefan Reiter +1 · 1 citation
Mathematics · Physics and Astronomy · #33C05 #33E30 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #math.DG #msc:33C05 #msc:33E30

paper · pdf · doi:10.48550/arxiv.0902.0760

14 pages

openalex publication_date 2009/02/04 · arxiv created 2012/04/17 · arxiv updated 2012/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a list of Heun equations which are Picard-Fuchs associated to families of algebraic varieties. Our list is based on the classification of families of elliptic curves with four singular fibers done by Herfurtner. We also show that pullbacks of hypergeometric functions by rational Belyi functions with restricted ramification data give rise to Heun equations.

Citations

• On reducing the Heun equation to the hypergeometric equation

Cited by

• A classification of coverings yielding Heun-to-hypergeometric reductions

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