BCOV ring and holomorphic anomaly equation

2008/10/27 by Shinobu Hosono, Hosono, Shinobu · 1 citation
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #hep-th #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.0810.4795

24 pages. v2, typos corrected. To appear in Advanced Studies in Pure Mathematics, "New developments in Algebraic Geometry, Integrable Systems and Mirror symmetry"; v3: eqs.(3.5) and (3.12) corrected. Minor corrections made accordingly

openalex publication_date 2008/10/27 · arxiv created 2013/09/12 · arxiv updated 2013/09/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study certain differential rings over the moduli space of Calabi-Yau manifolds. In the case of an elliptic curve, we observe a close relation to the differential ring of quasi-modular forms due to Kaneko and Zagier.

Citations

• Central charges, symplectic forms, and hypergeometric series in local mirror symmetry
• Higher genus Gromov-Witten invariants of the Grassmannian, and the Pfaffian Calabi-Yau threefolds

Cited by

• Resurgent structure of 2d Yang-Mills theory on a torus

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• Differential Rings from Special Kähler Geometry
• Polynomial Rings and Topological Strings
• Quasi-modular forms attached to elliptic curves, I
• BCOV rings on elliptic curves and eta function
• Gauss-Manin connection in disguise: Calabi-Yau threefolds