  We consider a family of generic weighted arrangements of $n$ hyperplanes in
$\C^k$ and show that the Gauss-Manin connection for the associated
hypergeometric integrals, the contravariant form on the space of singular
vectors, and the algebra of functions on the critical set of the master
function define a Frobenius like structure on the base of the family. As a
result of this construction we show that the matrix elements of the linear
operators of the Gauss-Manin connection are given by the 2k+1-st derivatives of
a single function on the base of the family, the function called the potential
of second kind, see formula (6.46).
