Let $F(x,y)$ be a bivariate polynomial, of degree $~n~$. Hence:
$$F(x,y) = \underset{i+j \leq n}{\sum_{i=0}\sum_{j=0}}~~a_{ij}~x^{i}~y^{j}$$
Can there exist an upperbound for the number of isolated zeros for $F(x,y)$ ? I understand that if we ask for number of zeros in general, it can be infinite. But by isolated zeros I mean that zeros that are not connected by a curve (on the $x-y$ plane).
I saw an answer to a similar question: Point 2 of this answer that one can bound the number of isolated zeros by $n^{2}$, or , it says some quadratic function of $n$. The answer was not elaborate to the point I could understand.
Can anyone kindly help me verify this ?