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I am studying commutative algebra from Atiyah's ' Introduction to Commutative Algebra' book but I am interested for algebraic geometry. My question is how much commutative algebra is needed for studying Hartshorne's algebraic geometry book? Thanks.

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  • $\begingroup$ How much commutative algebra do you need for this? Of course very much, see here. $\endgroup$ – Dietrich Burde May 9 '19 at 11:03
  • $\begingroup$ But can you please suggest me that which chapters from the starting of the contents will I follow from the Atiyah's book? $\endgroup$ – user454229 May 9 '19 at 11:08
  • $\begingroup$ No chapter will follow from Atiyah's book alone. But why don't you just start reading Hartshorne and look up something which you need then. See also this duplictate. $\endgroup$ – Dietrich Burde May 9 '19 at 11:14
  • $\begingroup$ Sooner or later everything from Atiyah-McDonald (and more) will be needed for a proper treatment of algebraic geometry. In my experience, though, the more advanced stuff (which is not in Atiyah-McDonald) is sometimes easier to learn once you understand why you need it, i.e. once you have some geometric intuition for the situation. I therefore suggest that you work through Atiyah-McDonald (which is really not that voluminous) and then proceed learning some algebraic geometry and go back to learning more advanced commutative algebra whenever it is needed. $\endgroup$ – asdq May 9 '19 at 11:18