Period matrices of algebraic varieties are important invariants which are defined as the matrices of the integrals of their de-Rham cohomology classes over singular homology classes. In this talk, we will present an explicit algorithmic formula between the period matrices of two algebraically different smooth projective complete intersection varieties with the same degree and same dimension (topologically same).

Our main tool is to use a deformation theory of certain homotopy algebras, called DGBV (differential Gerstenhaber Batalin-Vilkovisky) algebras attached to smooth projective complete intersections.

This is a joint work with Jeehoon Park (Postech).