# All homogeneous rings of a projective variety

This question is related to this one.

What I am wondering is if I have a graded ring $A$ such that $X=Proj(A)$, then is there some specific classification of $B$'s such that $X=Proj(B)$.

I am particularly interested in the case where $A=K[x_1,\ldots,x_n]/(\text{one homogeneous poly})$.