  In this paper, we introduce the notion of the diagonal property and the weak
point property for an ind-variety. We prove that the ind-varieties of higher
rank divisors of integral slopes on a smooth projective curve have the weak
point property. Moreover, we show that the ind-variety of $(1,n)$-divisors has
the diagonal property. Furthermore, we obtain that the Hilbert schemes
associated to the good partitions of a constant polynomial satisfy the diagonal
property. On the process of obtaining this, we provide an upper bound on the
number of such Hilbert schemes up to isomorphism. Furthermore, we prove that
the obtained upper bound is attained in case of genus zero curves and hence
conclude that the bound is sharp.

Algebraic Geometry