Arrangements and Frobenius like structures

Abstract

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 2 k + 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).