  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. In the process of obtaining this, we provide the exact number of such
Hilbert schemes up to isomorphism by proving that the multi symmetric products
associated to two distinct partitions of a positive integer $n$ are not
isomorphic.
