2020/08/14 by Murad Alim, Alim, Murad, Vadym Kurylenko +3
Mathematics · Physics and Astronomy · #14D07 #14J15 #14J32 #14J33 #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 #msc:14D07 #msc:14J15 #msc:14J32 #msc:14J33
paper · pdf · doi:10.48550/arxiv.2008.06523
26 pages. Expanded discussion in section 2. Proof of Proposition 4 was added. Typos were fixed and references added
openalex publication_date 2020/08/14 · arxiv created 2021/12/26 · arxiv updated 2021/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study moduli spaces of mirror non-compact Calabi-Yau threefolds enhanced with choices of differential forms. The differential forms are elements of the middle dimensional cohomology whose variation is described by a variation of mixed Hodge structures which is equipped with a flat Gauss-Manin connection. We construct graded differential rings of special functions on these moduli spaces and show that they contain rings of quasi-modular forms. We show that the algebra of derivations of quasi-modular forms can be obtained from the Gauss--Manin connection contracted with vector fields on the enhanced moduli spaces. We provide examples for this construction given by the mirrors of the canonical bundles of ℙ2 and \mathbbF2.