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KConrad
KConrad
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I'm not an algebraic geometrygeometer, but I do know several algebraic geometers and it's clear that modern algebraic geometry is a very large field some aspects of which involve technical modern abstractions (stacks!) others of which are in a more combinatorial direction (toric varieties, Grobner bases) and others involve more classical algebraic geometry.

However, I want to remake a point I made on my blog, which is that later on in your career you will be much better at learning things than you are now. As a result it's counterproductive to worry too much about what you should be learning now to maximize your efficiency of learning. Instead you should prioritize things you can learn now and which you enjoy learning now. Certainly you should start with an introductory algebraic geometry book, but once you're done with that there's no harm in looking at Eisenbud and seeing if you enjoy it. But if it's too hard going or if you feel like you're not fully appreciating it then go ahead and try reading something totally different. There'll be plenty of time to learn more commutative algebra while you're a grad student!

I'm not an algebraic geometry, but I do know several algebraic geometers and it's clear that modern algebraic geometry is a very large field some aspects of which involve technical modern abstractions (stacks!) others of which are in a more combinatorial direction (toric varieties, Grobner bases) and others involve more classical algebraic geometry.

However, I want to remake a point I made on my blog, which is that later on in your career you will be much better at learning things than you are now. As a result it's counterproductive to worry too much about what you should be learning now to maximize your efficiency of learning. Instead you should prioritize things you can learn now and which you enjoy learning now. Certainly you should start with an introductory algebraic geometry book, but once you're done with that there's no harm in looking at Eisenbud and seeing if you enjoy it. But if it's too hard going or if you feel like you're not fully appreciating it then go ahead and try reading something totally different. There'll be plenty of time to learn more commutative algebra while you're a grad student!

I'm not an algebraic geometer, but I do know several algebraic geometers and it's clear that modern algebraic geometry is a very large field some aspects of which involve technical modern abstractions (stacks!) others of which are in a more combinatorial direction (toric varieties, Grobner bases) and others involve more classical algebraic geometry.

However, I want to remake a point I made on my blog, which is that later on in your career you will be much better at learning things than you are now. As a result it's counterproductive to worry too much about what you should be learning now to maximize your efficiency of learning. Instead you should prioritize things you can learn now and which you enjoy learning now. Certainly you should start with an introductory algebraic geometry book, but once you're done with that there's no harm in looking at Eisenbud and seeing if you enjoy it. But if it's too hard going or if you feel like you're not fully appreciating it then go ahead and try reading something totally different. There'll be plenty of time to learn more commutative algebra while you're a grad student!

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Noah Snyder
Noah Snyder
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I'm not an algebraic geometry, but I do know several algebraic geometers and it's clear that modern algebraic geometry is a very large field some aspects of which involve technical modern abstractions (stacks!) others of which are in a more combinatorial direction (toric varieties, Grobner bases) and others involve more classical algebraic geometry.

However, I want to remake a point I made on my blog, which is that later on in your career you will be much better at learning things than you are now. As a result it's counterproductive to worry too much about what you should be learning now to maximize your efficiency of learning. Instead you should prioritize things you can learn now and which you enjoy learning now. Certainly you should start with an introductory algebraic geometry book, but once you're done with that there's no harm in looking at Eisenbud and seeing if you enjoy it. But if it's too hard going or if you feel like you're not fully appreciating it then go ahead and try reading something totally different. There'll be plenty of time to learn more commutative algebra while you're a grad student!