Differential Rings from Special Kähler Geometry

2013/10/14 by Jie Zhou, Zhou, Jie · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.1310.3555

reference added, typos corrected

openalex publication_date 2013/10/14 · arxiv created 2014/11/26 · arxiv updated 2014/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study triples of graded rings defined over the deformation spaces for certain one-parameter families of Calabi-Yau threefolds. These rings are analogues of the rings of modular forms, quasi-modular forms and almost-holomorphic modular forms. We also discuss some of their applications in solving the holomorphic anomaly equations.

Citations

• Local Mirror Symmetry at Higher Genus

Cited by

• Algebraic structure of tt^* equations for Calabi-Yau sigma models

Related

• BCOV ring and holomorphic anomaly equation
• The algebra of derivations of quasi-modular forms from mirror symmetry
• Polynomial Rings and Topological Strings
• Quasi-isometry and deformations of Calabi-Yau manifolds
• Gauss-Manin connection in disguise: Calabi-Yau threefolds