I'm looking for a book about the geometry of polynomial rings. I often see in some seminars the presenters have some geometric intuition when they look at the quotient by an ideal. For example, by looking at the graph $z^2=xy$ we can understand something about $k[x,y,z]/(xy-z^2)$, like it is a domain.
My professor recommends me the book Undergraduate COmmmutative Algebra but so far I don't think it has what I want. I know this is a vague question but do you have any recommendation?