We will consider deformation of period integrals for complex algebraic varieties, especially projective complete intersection. We get an deformation 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).