I have a system of complex polynomials equal to zero with $n$ variables and each polynomials is homogeneous in degree. There are $m$ polynomials and $m>n$. So the system is overdetermined. Since all polynomials are homogeneous, I think zero is one of the solution of the system. But I don't know if there are more than one solutions. So I would like to ask what are the condition for such kind of system to admit unique solution?
So my question is, what are the conditions for a overdetermined system of homogeneous polynomials admit unique solution, which is zero?