Can anyone offer advice on roughly how much commutative algebra, homological algebra etc. one needs to know to do research in (or to learn) modern algebraic geometry. Would you need to be familiar with something like the contents of Eisenbud's Commutative Algebra: With a View Toward Algebraic Geometry, or is less needed in reality? (I am familiar with more commutative algebra than that which is covered in Atiyah and MacDonald's *Introduction to Commutative Algebra", but less than that which is covered in Eisenbud's textbook.)

Also, is modern algebraic geometry concerned with abstractions such as schemes, sheaves, topological spaces, commutative and noncommutative rings etc., or is it just classical algebraic geometry in an abstract form? Perhaps more specifically, to do research in modern algebraic geometry, do you need to be familiar with classical algebraic geometry, or is it possible to think of algebraic geometry as an "abstract language" and do research based just on this perception?

While I suspect that, as with other branches of mathematics, "abstraction was invented to analyze the concrete", with all the emphasis currently given to the understanding of abstract tools, for someone who is not very familiar with the subject (such as myself), it seems that algebraic geometry is a "mixture" of general topology and abstract algebra. Is this right? If not, succinctly my question is: how great an influence does classical algebraic geometry have on modern algebraic geometry today?