  We consider a polynomial h(x,y) in two complex variables of degree n+1>1 with
a generic higher homogeneous part. The rank of the first homology group of its
nonsingular level curve h(x,y)=t is n*n. To each 1- form in the variable space
and a generator of the homology group one associates the (Abelian) integral of
the form along the generator. The Abelian integral is a multivalued function in
t. For a fixed canonic tuple of n*n monomial 1- forms we consider the
multivalued square matrix function in t whose elements are the Abelian
integrals of the forms along the generators. Its determinant does not depend on
the choice of the generators in the homology group (up to change of sign, which
corresponds to change of generator system that reverses orientation).
  In 1999 Yu.S.Ilyashenko proved that the determinant of the Abelian integral
matrix is a polynomial in t of degree n*n whose zeroes are the critical values
of h. We give an explicit formula for the determinant.
