TÃtulo: Rankin-Cohen bracket for Calabi-Yau modular forms
Autor: Younes NIKDELAN (UERJ)
Date: 10:30 05/06/2020
Modularity of CY manifolds is still a great challenge in arithmetic algebraic geometry. In this direction, Movasati introduced a generalization of (quasi-)modular forms called CY modular forms. In this talk we present some evidences in favour of this generalization. More precisely, for any positive integer $n$, we consider the modular vector field $\sf R$ on the moduli space $\sf T$ of the CY $n$-folds arising from the Dwork family and enhanced with a certain basis of the $n$-th algebraic de Rham cohomology. Here, by the CY modular forms we mean algebraic combinations of the components of a particular solution of $\sf R$ which are provided with natural weights. We observe that there exists a canonical Rankin-Cohen algebra structure on the space of CY modular forms, and show that there exists a proper subspace of the space of CY modular forms which is closed under the Rankin-Cohen brackets.