An explicit formula for period determinant
In this paper the author calculates the determinant of the period matrix associated to a generic complex polynomial in two variables \(H(x,y)\), a basis in the first cohomology group of a nonsingular level curve of \(H\) and a set of complex homogeneous polynomial 1-forms. An explicit formula for the period determinant has been computed before by A. N. Varchenko, but only up to a constant factor depending on the degree of the polynomial. In the present paper the author computes the constant factor. The computations are made gradually, first for a special form set and then for the general case.
scientific article; zbMATH DE number 5145714