  Variables of separation for classical $GL(3)$ magnetic chain obtained by
Sklyanin form a generic positive divisor $D$ of degree $n$ on a genus $g$
non-hyperelliptic algebraic curve. Because $n>g$ this divisor $D$ has unique
representative $\rho(D)$ in the Jacobian which can be constructed by using
dim$|D|=n-g$ steps of Abel's algorithm. We study properties of the
corresponding chain of divisors and prove that the classical $GL(3)$ magnetic
chain is a superintegrable system with dim$|D|=2$ superintegrable Hamiltonians.
