On symplectically rigid local systems of rank four and Calabi-Yau operators

2011/05/05 by Michael Bogner, Bogner, Michael, Stefan Reiter +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Finite Group Theory Research #math.AG #math.CA

paper · pdf · doi:10.48550/arxiv.1105.1136

arxiv created 2011/05/05 · openalex publication_date 2011/05/05 · arxiv updated 2011/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify all \Sp₄(ℂ)-rigid, quasi-unipotent local systems and show that all of them have geometric origin. Furthermore, we investigate which of those having a maximal unipotent element are induced by fourth order Calabi-Yau operators. Via this approach, we reconstruct all known Calabi-Yau operators inducing a \Sp₄(ℂ)-rigid monodromy tuple and obtain closed formulae for special solutions of them.

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• On the construction of Calabi-Yau operators

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