Prerequisites for book “mirror symmetry and algebraic geometry” by Cox and Katz The 2019 Stack Overflow Developer Survey Results Are In Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)What are the required backgrounds of Robin Hartshorne's Algebraic Geometry book?Mathematics and Physics prerequisites for mirror symmetryPrerequisites for Bredon's “Topology and Geometry”?Question about Qing Liu's Algebraic Geometry bookWhat to study from Eisenbud's Commutative Algebra to prepare for Hartshorne's Algebraic Geometry?Prerequisites for Hartshorne: Euclid and beyond?Prerequisites for Vakil's “Foundations of Algebraic Geometry” (Or other texts)References request for prerequisites of topology and differential geometryBook recommendations for algebraic number theory with usage of algebraic geometryFoliations and groupoids in algebraic geometry
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Prerequisites for book “mirror symmetry and algebraic geometry” by Cox and Katz
The 2019 Stack Overflow Developer Survey Results Are In
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)What are the required backgrounds of Robin Hartshorne's Algebraic Geometry book?Mathematics and Physics prerequisites for mirror symmetryPrerequisites for Bredon's “Topology and Geometry”?Question about Qing Liu's Algebraic Geometry bookWhat to study from Eisenbud's Commutative Algebra to prepare for Hartshorne's Algebraic Geometry?Prerequisites for Hartshorne: Euclid and beyond?Prerequisites for Vakil's “Foundations of Algebraic Geometry” (Or other texts)References request for prerequisites of topology and differential geometryBook recommendations for algebraic number theory with usage of algebraic geometryFoliations and groupoids in algebraic geometry
$begingroup$
As the title suggest, I am trying to read the book mentioned, but I find that it uses a lot of material that I don't know yet. For example, it uses toric geometry and polytopes, topics that I've never seen in regular courses at my university.
So, I want to know from the experience of someone who has used the book, what are the prerequisites of algebraic geometry to understand the text. Is it necessary to know the language of schemes? Are schemes used at all?
My background is very modest, being a course in classic algebraic geometry, at the level of Fulton's book "Algebraic curves" and almost the second chapter of Hartshorne's "Algebraic Geometry".
I found the book too diffuse, as to the range of topics used is refered. If someone can answer my questions and give some suitable references (in terms of what is needed in the book) for the necessary background, I'll be very grateful. The thing is, I barely can see what is being done with the algebraic geometry in the text, and I'm looking for an "scheme theoretic" point of view of the topic.
algebraic-geometry reference-request mirror-symmetry
edited Mar 25 at 7:34
Andrews
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
$endgroup$
add a comment |
$begingroup$
As the title suggest, I am trying to read the book mentioned, but I find that it uses a lot of material that I don't know yet. For example, it uses toric geometry and polytopes, topics that I've never seen in regular courses at my university.
So, I want to know from the experience of someone who has used the book, what are the prerequisites of algebraic geometry to understand the text. Is it necessary to know the language of schemes? Are schemes used at all?
My background is very modest, being a course in classic algebraic geometry, at the level of Fulton's book "Algebraic curves" and almost the second chapter of Hartshorne's "Algebraic Geometry".
I found the book too diffuse, as to the range of topics used is refered. If someone can answer my questions and give some suitable references (in terms of what is needed in the book) for the necessary background, I'll be very grateful. The thing is, I barely can see what is being done with the algebraic geometry in the text, and I'm looking for an "scheme theoretic" point of view of the topic.
algebraic-geometry reference-request mirror-symmetry
edited Mar 25 at 7:34
Andrews
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
$endgroup$
$begingroup$
It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59
add a comment |
$begingroup$
As the title suggest, I am trying to read the book mentioned, but I find that it uses a lot of material that I don't know yet. For example, it uses toric geometry and polytopes, topics that I've never seen in regular courses at my university.
So, I want to know from the experience of someone who has used the book, what are the prerequisites of algebraic geometry to understand the text. Is it necessary to know the language of schemes? Are schemes used at all?
My background is very modest, being a course in classic algebraic geometry, at the level of Fulton's book "Algebraic curves" and almost the second chapter of Hartshorne's "Algebraic Geometry".
I found the book too diffuse, as to the range of topics used is refered. If someone can answer my questions and give some suitable references (in terms of what is needed in the book) for the necessary background, I'll be very grateful. The thing is, I barely can see what is being done with the algebraic geometry in the text, and I'm looking for an "scheme theoretic" point of view of the topic.
algebraic-geometry reference-request mirror-symmetry
edited Mar 25 at 7:34
Andrews
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
$endgroup$
As the title suggest, I am trying to read the book mentioned, but I find that it uses a lot of material that I don't know yet. For example, it uses toric geometry and polytopes, topics that I've never seen in regular courses at my university.
So, I want to know from the experience of someone who has used the book, what are the prerequisites of algebraic geometry to understand the text. Is it necessary to know the language of schemes? Are schemes used at all?
My background is very modest, being a course in classic algebraic geometry, at the level of Fulton's book "Algebraic curves" and almost the second chapter of Hartshorne's "Algebraic Geometry".
I found the book too diffuse, as to the range of topics used is refered. If someone can answer my questions and give some suitable references (in terms of what is needed in the book) for the necessary background, I'll be very grateful. The thing is, I barely can see what is being done with the algebraic geometry in the text, and I'm looking for an "scheme theoretic" point of view of the topic.
algebraic-geometry reference-request mirror-symmetry
algebraic-geometry reference-request mirror-symmetry
edited Mar 25 at 7:34
Andrews
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
edited Mar 25 at 7:34
Andrews
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
edited Mar 25 at 7:34
Andrews
1,2962423
edited Mar 25 at 7:34
Andrews
1,2962423
edited Mar 25 at 7:34
Andrews
1,2962423
1,2962423
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
asked Oct 10 '16 at 22:51
Daniel MejiaDaniel Mejia
30319
30319
$begingroup$
It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59
add a comment |
$begingroup$
It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59
$begingroup$
It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59
$begingroup$
It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59
add a comment |
1 Answer
1
active
oldest
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$begingroup$
I was reading it a year ago. It's important that you have a little experience with Hodge decomposition, Gauss-Manin connection and Kahler geometry in general (there are two volumes of Claire Voisin which provide the necessary background. Here's a review). Also you need to understand moduli space of algebraic curves (read for examples Morris and Harrison's "Moduli of curves". Virtual fundamental class is a stack-theoretic construction and thus has some relationship to schemes but I don't think it's important for a first read- so schemes are not important). Fulton has a book on toric varieties, you can also look at Batyrev's original work. Also you need to understand group actions on varieties and orbifold construction- I'm not really sure about reference for that. As for physical side (string theory or QFT) it is not really important but you can look through Clay monograph's physics chapters.
$endgroup$
add a comment |
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1 Answer
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1 Answer
1
active
oldest
votes
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oldest
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votes
$begingroup$
I was reading it a year ago. It's important that you have a little experience with Hodge decomposition, Gauss-Manin connection and Kahler geometry in general (there are two volumes of Claire Voisin which provide the necessary background. Here's a review). Also you need to understand moduli space of algebraic curves (read for examples Morris and Harrison's "Moduli of curves". Virtual fundamental class is a stack-theoretic construction and thus has some relationship to schemes but I don't think it's important for a first read- so schemes are not important). Fulton has a book on toric varieties, you can also look at Batyrev's original work. Also you need to understand group actions on varieties and orbifold construction- I'm not really sure about reference for that. As for physical side (string theory or QFT) it is not really important but you can look through Clay monograph's physics chapters.
$endgroup$
add a comment |
$begingroup$
I was reading it a year ago. It's important that you have a little experience with Hodge decomposition, Gauss-Manin connection and Kahler geometry in general (there are two volumes of Claire Voisin which provide the necessary background. Here's a review). Also you need to understand moduli space of algebraic curves (read for examples Morris and Harrison's "Moduli of curves". Virtual fundamental class is a stack-theoretic construction and thus has some relationship to schemes but I don't think it's important for a first read- so schemes are not important). Fulton has a book on toric varieties, you can also look at Batyrev's original work. Also you need to understand group actions on varieties and orbifold construction- I'm not really sure about reference for that. As for physical side (string theory or QFT) it is not really important but you can look through Clay monograph's physics chapters.
$endgroup$
add a comment |
$begingroup$
I was reading it a year ago. It's important that you have a little experience with Hodge decomposition, Gauss-Manin connection and Kahler geometry in general (there are two volumes of Claire Voisin which provide the necessary background. Here's a review). Also you need to understand moduli space of algebraic curves (read for examples Morris and Harrison's "Moduli of curves". Virtual fundamental class is a stack-theoretic construction and thus has some relationship to schemes but I don't think it's important for a first read- so schemes are not important). Fulton has a book on toric varieties, you can also look at Batyrev's original work. Also you need to understand group actions on varieties and orbifold construction- I'm not really sure about reference for that. As for physical side (string theory or QFT) it is not really important but you can look through Clay monograph's physics chapters.
$endgroup$
I was reading it a year ago. It's important that you have a little experience with Hodge decomposition, Gauss-Manin connection and Kahler geometry in general (there are two volumes of Claire Voisin which provide the necessary background. Here's a review). Also you need to understand moduli space of algebraic curves (read for examples Morris and Harrison's "Moduli of curves". Virtual fundamental class is a stack-theoretic construction and thus has some relationship to schemes but I don't think it's important for a first read- so schemes are not important). Fulton has a book on toric varieties, you can also look at Batyrev's original work. Also you need to understand group actions on varieties and orbifold construction- I'm not really sure about reference for that. As for physical side (string theory or QFT) it is not really important but you can look through Clay monograph's physics chapters.
answered Jan 22 '17 at 10:21
user285001
add a comment |
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It seems that they assume some background in Kahler manifold and symplectic manifold.
$endgroup$
– user99914
Oct 10 '16 at 22:59