Reference for flag varieties G/P
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Is there a good reference for learning about flag varieties $G/P$? I'm already comfortable with the algebraic geometry and the example of Grassmannians, but I am not so comfortable with algebraic groups aside from basic Lie theory.
For example, it would be nice to know which properties of the Grassmannian extend to more general $G/P$ (decomposition into Schubert cells, rules for intersecting classes, the Picard group and the Plücker embedding), so I know what sorts of arguments generalize cheaply and what arguments do not.
algebraic-geometry reference-request representation-theory schubert-calculus
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
$endgroup$
add a comment |
$begingroup$
Is there a good reference for learning about flag varieties $G/P$? I'm already comfortable with the algebraic geometry and the example of Grassmannians, but I am not so comfortable with algebraic groups aside from basic Lie theory.
For example, it would be nice to know which properties of the Grassmannian extend to more general $G/P$ (decomposition into Schubert cells, rules for intersecting classes, the Picard group and the Plücker embedding), so I know what sorts of arguments generalize cheaply and what arguments do not.
algebraic-geometry reference-request representation-theory schubert-calculus
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
$endgroup$
2
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
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Over what field?
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– Moishe Cohen
Dec 17 '17 at 6:36
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Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35
add a comment |
$begingroup$
Is there a good reference for learning about flag varieties $G/P$? I'm already comfortable with the algebraic geometry and the example of Grassmannians, but I am not so comfortable with algebraic groups aside from basic Lie theory.
For example, it would be nice to know which properties of the Grassmannian extend to more general $G/P$ (decomposition into Schubert cells, rules for intersecting classes, the Picard group and the Plücker embedding), so I know what sorts of arguments generalize cheaply and what arguments do not.
algebraic-geometry reference-request representation-theory schubert-calculus
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
$endgroup$
Is there a good reference for learning about flag varieties $G/P$? I'm already comfortable with the algebraic geometry and the example of Grassmannians, but I am not so comfortable with algebraic groups aside from basic Lie theory.
For example, it would be nice to know which properties of the Grassmannian extend to more general $G/P$ (decomposition into Schubert cells, rules for intersecting classes, the Picard group and the Plücker embedding), so I know what sorts of arguments generalize cheaply and what arguments do not.
algebraic-geometry reference-request representation-theory schubert-calculus
algebraic-geometry reference-request representation-theory schubert-calculus
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
edited Dec 25 '18 at 11:46
Matt Samuel
38.8k63769
38.8k63769
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
asked Dec 15 '17 at 16:33
DCTDCT
1,7921020
1,7921020
2
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
$begingroup$
Over what field?
$endgroup$
– Moishe Cohen
Dec 17 '17 at 6:36
$begingroup$
Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35
add a comment |
2
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
$begingroup$
Over what field?
$endgroup$
– Moishe Cohen
Dec 17 '17 at 6:36
$begingroup$
Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35
2
2
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
$begingroup$
Over what field?
$endgroup$
– Moishe Cohen
Dec 17 '17 at 6:36
$begingroup$
Over what field?
$endgroup$
– Moishe Cohen
Dec 17 '17 at 6:36
$begingroup$
Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35
$begingroup$
Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35
add a comment |
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2
$begingroup$
I personally liked Michel Brion's notes on the topic.
$endgroup$
– Jesko Hüttenhain
Dec 16 '17 at 9:05
$begingroup$
Over what field?
$endgroup$
– Moishe Cohen
Dec 17 '17 at 6:36
$begingroup$
Jesko: Thanks, I'll print those notes out now Moishe: I don't even know the story over the complex numbers, but getting to know what is different in positive characteristic is useful as well.
$endgroup$
– DCT
Dec 17 '17 at 18:35