Roadmap to study Algebraic Geometry [duplicate]
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This question already has an answer here:
road map to learn algebraic geometry
2 answers
I have completed Masters in Mathematics.
I want to study Algebraic Geometry.
How to get a taste of algebraic geometry at the Introductory Level?
I found there are many books on this subject all written by Great Authors.
But my question is:
What are the backgrounds needed to study Algebraic Geometry at the Graduate level?
What are the books that start from scratch?
Can someone please give a list of books starting from Introductory level to Pursuing Research in Graduate study?
algebraic-geometry reference-request soft-question book-recommendation
edited Jan 9 at 5:42
Kemono Chen
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
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marked as duplicate by Adrian Keister, jgon, José Carlos Santos, KReiser, amWhy Jan 9 at 19:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
add a comment |
$begingroup$
This question already has an answer here:
road map to learn algebraic geometry
2 answers
I have completed Masters in Mathematics.
I want to study Algebraic Geometry.
How to get a taste of algebraic geometry at the Introductory Level?
I found there are many books on this subject all written by Great Authors.
But my question is:
What are the backgrounds needed to study Algebraic Geometry at the Graduate level?
What are the books that start from scratch?
Can someone please give a list of books starting from Introductory level to Pursuing Research in Graduate study?
algebraic-geometry reference-request soft-question book-recommendation
edited Jan 9 at 5:42
Kemono Chen
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
$endgroup$
marked as duplicate by Adrian Keister, jgon, José Carlos Santos, KReiser, amWhy Jan 9 at 19:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09
add a comment |
$begingroup$
This question already has an answer here:
road map to learn algebraic geometry
2 answers
I have completed Masters in Mathematics.
I want to study Algebraic Geometry.
How to get a taste of algebraic geometry at the Introductory Level?
I found there are many books on this subject all written by Great Authors.
But my question is:
What are the backgrounds needed to study Algebraic Geometry at the Graduate level?
What are the books that start from scratch?
Can someone please give a list of books starting from Introductory level to Pursuing Research in Graduate study?
algebraic-geometry reference-request soft-question book-recommendation
edited Jan 9 at 5:42
Kemono Chen
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
$endgroup$
This question already has an answer here:
road map to learn algebraic geometry
2 answers
I have completed Masters in Mathematics.
I want to study Algebraic Geometry.
How to get a taste of algebraic geometry at the Introductory Level?
I found there are many books on this subject all written by Great Authors.
But my question is:
What are the backgrounds needed to study Algebraic Geometry at the Graduate level?
What are the books that start from scratch?
Can someone please give a list of books starting from Introductory level to Pursuing Research in Graduate study?
This question already has an answer here:
road map to learn algebraic geometry
2 answers
algebraic-geometry reference-request soft-question book-recommendation
algebraic-geometry reference-request soft-question book-recommendation
edited Jan 9 at 5:42
Kemono Chen
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
edited Jan 9 at 5:42
Kemono Chen
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
edited Jan 9 at 5:42
Kemono Chen
2,8831739
edited Jan 9 at 5:42
Kemono Chen
2,8831739
edited Jan 9 at 5:42
Kemono Chen
2,8831739
2,8831739
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
asked Jan 9 at 5:28
LearnmoreLearnmore
17.6k32495
17.6k32495
marked as duplicate by Adrian Keister, jgon, José Carlos Santos, KReiser, amWhy Jan 9 at 19:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
marked as duplicate by Adrian Keister, jgon, José Carlos Santos, KReiser, amWhy Jan 9 at 19:57
This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09
add a comment |
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
I was pretty much in the same position you are in about a year an a half ago, and I have a great deal to learn. Algebraic geometry is a massive and deep subject. Hopefully, you'll enjoy it!
Background: I would say that the main things you will need are some background in commutative algebra, and some knowledge of basic topology. A bit of familiarity with the language of category theory is not strictly necessary in the beginning, but it does go some way to view objects in the context of already known structures.
Books to start from scratch with:
- "Basic Algebraic Geometry 1" by Igor Shafarevich might be a good place to start.
- "Commutative Algebra: with a View Toward Algebraic Geometry" by Eisenbud & Harris is also a good resource to pick up some algebraic background with an explicit geometric focus.
- I would also recommend "Undergraduate Algebraic Geometry" by David Mumford.
Concerning your third category:
- "Algebraic Geometry" by Robin Hartshorne is probably the most famous book in the field. However, there are quite a few people who tend to be wary of it because it can be a bit difficult to read. However, I highly recommend that this book play some role in your reading.
- "Algebraic Geometry I - Schemes With Examples & Exercises" by Görtz & Wedhorn is also a very good resource. Its focus is schemes, but it does begin with much introductory material. Its appendices are also of note.
- I would also suggest the notes of Andreas Gathmann, which can be found freely online.
- Finally, I would be remiss if I did not suggest the famous notes of Ravi Vakil which he has made freely available online. These notes undergo continual expansion, and improvement.
Beyond the requirements of your question, allow me to suggest " The Geometry of Schemes" by Eisenbud & Harris. The focus is again scheme theory, but it is a very good resource for studying scheme theory should you choose to venture deeper into AG.
Best of luck to you.
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
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add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I was pretty much in the same position you are in about a year an a half ago, and I have a great deal to learn. Algebraic geometry is a massive and deep subject. Hopefully, you'll enjoy it!
Background: I would say that the main things you will need are some background in commutative algebra, and some knowledge of basic topology. A bit of familiarity with the language of category theory is not strictly necessary in the beginning, but it does go some way to view objects in the context of already known structures.
Books to start from scratch with:
- "Basic Algebraic Geometry 1" by Igor Shafarevich might be a good place to start.
- "Commutative Algebra: with a View Toward Algebraic Geometry" by Eisenbud & Harris is also a good resource to pick up some algebraic background with an explicit geometric focus.
- I would also recommend "Undergraduate Algebraic Geometry" by David Mumford.
Concerning your third category:
- "Algebraic Geometry" by Robin Hartshorne is probably the most famous book in the field. However, there are quite a few people who tend to be wary of it because it can be a bit difficult to read. However, I highly recommend that this book play some role in your reading.
- "Algebraic Geometry I - Schemes With Examples & Exercises" by Görtz & Wedhorn is also a very good resource. Its focus is schemes, but it does begin with much introductory material. Its appendices are also of note.
- I would also suggest the notes of Andreas Gathmann, which can be found freely online.
- Finally, I would be remiss if I did not suggest the famous notes of Ravi Vakil which he has made freely available online. These notes undergo continual expansion, and improvement.
Beyond the requirements of your question, allow me to suggest " The Geometry of Schemes" by Eisenbud & Harris. The focus is again scheme theory, but it is a very good resource for studying scheme theory should you choose to venture deeper into AG.
Best of luck to you.
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
$endgroup$
add a comment |
$begingroup$
I was pretty much in the same position you are in about a year an a half ago, and I have a great deal to learn. Algebraic geometry is a massive and deep subject. Hopefully, you'll enjoy it!
Background: I would say that the main things you will need are some background in commutative algebra, and some knowledge of basic topology. A bit of familiarity with the language of category theory is not strictly necessary in the beginning, but it does go some way to view objects in the context of already known structures.
Books to start from scratch with:
- "Basic Algebraic Geometry 1" by Igor Shafarevich might be a good place to start.
- "Commutative Algebra: with a View Toward Algebraic Geometry" by Eisenbud & Harris is also a good resource to pick up some algebraic background with an explicit geometric focus.
- I would also recommend "Undergraduate Algebraic Geometry" by David Mumford.
Concerning your third category:
- "Algebraic Geometry" by Robin Hartshorne is probably the most famous book in the field. However, there are quite a few people who tend to be wary of it because it can be a bit difficult to read. However, I highly recommend that this book play some role in your reading.
- "Algebraic Geometry I - Schemes With Examples & Exercises" by Görtz & Wedhorn is also a very good resource. Its focus is schemes, but it does begin with much introductory material. Its appendices are also of note.
- I would also suggest the notes of Andreas Gathmann, which can be found freely online.
- Finally, I would be remiss if I did not suggest the famous notes of Ravi Vakil which he has made freely available online. These notes undergo continual expansion, and improvement.
Beyond the requirements of your question, allow me to suggest " The Geometry of Schemes" by Eisenbud & Harris. The focus is again scheme theory, but it is a very good resource for studying scheme theory should you choose to venture deeper into AG.
Best of luck to you.
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
$endgroup$
add a comment |
$begingroup$
I was pretty much in the same position you are in about a year an a half ago, and I have a great deal to learn. Algebraic geometry is a massive and deep subject. Hopefully, you'll enjoy it!
Background: I would say that the main things you will need are some background in commutative algebra, and some knowledge of basic topology. A bit of familiarity with the language of category theory is not strictly necessary in the beginning, but it does go some way to view objects in the context of already known structures.
Books to start from scratch with:
- "Basic Algebraic Geometry 1" by Igor Shafarevich might be a good place to start.
- "Commutative Algebra: with a View Toward Algebraic Geometry" by Eisenbud & Harris is also a good resource to pick up some algebraic background with an explicit geometric focus.
- I would also recommend "Undergraduate Algebraic Geometry" by David Mumford.
Concerning your third category:
- "Algebraic Geometry" by Robin Hartshorne is probably the most famous book in the field. However, there are quite a few people who tend to be wary of it because it can be a bit difficult to read. However, I highly recommend that this book play some role in your reading.
- "Algebraic Geometry I - Schemes With Examples & Exercises" by Görtz & Wedhorn is also a very good resource. Its focus is schemes, but it does begin with much introductory material. Its appendices are also of note.
- I would also suggest the notes of Andreas Gathmann, which can be found freely online.
- Finally, I would be remiss if I did not suggest the famous notes of Ravi Vakil which he has made freely available online. These notes undergo continual expansion, and improvement.
Beyond the requirements of your question, allow me to suggest " The Geometry of Schemes" by Eisenbud & Harris. The focus is again scheme theory, but it is a very good resource for studying scheme theory should you choose to venture deeper into AG.
Best of luck to you.
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
$endgroup$
I was pretty much in the same position you are in about a year an a half ago, and I have a great deal to learn. Algebraic geometry is a massive and deep subject. Hopefully, you'll enjoy it!
Background: I would say that the main things you will need are some background in commutative algebra, and some knowledge of basic topology. A bit of familiarity with the language of category theory is not strictly necessary in the beginning, but it does go some way to view objects in the context of already known structures.
Books to start from scratch with:
- "Basic Algebraic Geometry 1" by Igor Shafarevich might be a good place to start.
- "Commutative Algebra: with a View Toward Algebraic Geometry" by Eisenbud & Harris is also a good resource to pick up some algebraic background with an explicit geometric focus.
- I would also recommend "Undergraduate Algebraic Geometry" by David Mumford.
Concerning your third category:
- "Algebraic Geometry" by Robin Hartshorne is probably the most famous book in the field. However, there are quite a few people who tend to be wary of it because it can be a bit difficult to read. However, I highly recommend that this book play some role in your reading.
- "Algebraic Geometry I - Schemes With Examples & Exercises" by Görtz & Wedhorn is also a very good resource. Its focus is schemes, but it does begin with much introductory material. Its appendices are also of note.
- I would also suggest the notes of Andreas Gathmann, which can be found freely online.
- Finally, I would be remiss if I did not suggest the famous notes of Ravi Vakil which he has made freely available online. These notes undergo continual expansion, and improvement.
Beyond the requirements of your question, allow me to suggest " The Geometry of Schemes" by Eisenbud & Harris. The focus is again scheme theory, but it is a very good resource for studying scheme theory should you choose to venture deeper into AG.
Best of luck to you.
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
answered Jan 9 at 15:48
Overwhelmed AG ApprenticeOverwhelmed AG Apprentice
267
267
add a comment |
add a comment |
$begingroup$
Relevant MO threads: mathoverflow.net/q/1291 and mathoverflow.net/q/35288 .
$endgroup$
– André 3000
Jan 9 at 6:09