Topology of algebraic variety

Question

I have an algebraic variety given by a polynomial $1+x(1+y)^2$ over $\mathbb C$. Is there any reasonable way to see how topologically the algebraic variety defined by this polynomial looks like?

Answer 1

The open sets of that variety are the variety itself take away finite number of (algebraic) curves and points. Is this what you mean by "topologically see"?