turkmath.org

In this talk, we will discuss concrete monodromy group representation of the solution space to Picard-Fuchs equation for the period integrals associated to an affine complete intersection variety. Our main interest will be focused on several cases where the concrete monodromy representation of the solutions is available. As an example of our investigations on Horn type hypergeometric functions (or Gel’fand-Kapranov-Zelevinsky A-Hypergeometric functions), we show the following. Let $Y$ be a Calabi-Yau complete intersection in a weighted projective space. The space of Hermitian quadratic invariants of the hypergeometric monodromy group associated with the period integrals of the mirror CI variety $X$ to $Y$ is one-dimensional and spanned by the Gram matrix of a split-generator of the derived category of coherent sheaves on $Y$ with respect to the Euler form. We shall discuss the question concerning the arithmeticity of the above monodromy group.