BCOV cusp forms of lattice polarized K3 surfaces

2023/03/08 by Shinobu Hosono, Hosono, Shinobu, Atsushi Kanazawa +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2303.04383

openalex publication_date 2023/03/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the BCOV formula for the lattice polarized K3 surfaces. We find that it yields cusp forms expressed by certain eta products for many families of rank 19 lattice polarized K3 surfaces over ℙ¹. Moreover, for Clingher-Doran's family of U⊕ E₈(-1)⊕ E₇(-1)-polarized K3 surfaces, we obtain the Igusa cusp forms χ₁₀ and χ₁₂ from the formula. Inspired by the arithmetic properties of mirror maps studied by Lian-Yau, we also derive the K3 differential operators for all the genus zero groups of type Γ₀(n)₊.

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