A SURVEY ON MODULAR VECTOR FIELDS AND CY MODULAR FORMS ATTACHED TO DWORK FAMILY
DOI:
https://doi.org/10.12957/cadmat.2021.63348Resumo
This article aimes to give a survay of the works of the author on modular vector fields and Calabi-Yau (CY) modular forms attached to the Dwork family. It is mostly tried to be more objective and avoid technical details. For any positive integer $n$, it is firstly introduced an enhanced moduli space $\textsf{T}:=\textsf{T}_n$ of CY $n$-folds arising from the Dwork family. It is observed that there exists a unique vector field $\textsf{D}$ in $\textsf{T}$, known as modular vector field, whose solution components can be expressed as $q$-expansions (Fourier series) with integer coefficients. We call these $q$-expansions CY modular forms and it is verified that the space generated by them has a canonical $\mathfrak{sl}_2(\mathbb{C})$-module structure which provides it with a Rankin-Cohen algebraic structure. All these concepts are explicitly established for $n=1,2,3,4$.Downloads
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Publicado
2021-12-17
Como Citar
Nikdelan, Y. (2021). A SURVEY ON MODULAR VECTOR FIELDS AND CY MODULAR FORMS ATTACHED TO DWORK FAMILY. Cadernos Do IME - Série Matemática, (17), 100–112. https://doi.org/10.12957/cadmat.2021.63348
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Artigos de Divulgação
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