Schubert calculus and number of lines satisfying some properties.
$begingroup$
I am reading the file. I have a question on pae 18. It is said that: Given a line in $mathbb{R}^3$, the family of lines intersecting it can be interpreted in $G(2, 4)$ as the Schubert variety
$$
X_{{2,4}}=overline{left(begin{matrix}
* & 1 & 0 & 0 \
* & 0 & * & 1
end{matrix}right)}
$$
with respect to a suitably chosen basis determined by the line.
Why the family of lines is $X_{{2,4}}$? Thank you very much.
geometry algebraic-geometry representation-theory schubert-calculus
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
$endgroup$
add a comment |
$begingroup$
I am reading the file. I have a question on pae 18. It is said that: Given a line in $mathbb{R}^3$, the family of lines intersecting it can be interpreted in $G(2, 4)$ as the Schubert variety
$$
X_{{2,4}}=overline{left(begin{matrix}
* & 1 & 0 & 0 \
* & 0 & * & 1
end{matrix}right)}
$$
with respect to a suitably chosen basis determined by the line.
Why the family of lines is $X_{{2,4}}$? Thank you very much.
geometry algebraic-geometry representation-theory schubert-calculus
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
$endgroup$
$begingroup$
I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15
add a comment |
$begingroup$
I am reading the file. I have a question on pae 18. It is said that: Given a line in $mathbb{R}^3$, the family of lines intersecting it can be interpreted in $G(2, 4)$ as the Schubert variety
$$
X_{{2,4}}=overline{left(begin{matrix}
* & 1 & 0 & 0 \
* & 0 & * & 1
end{matrix}right)}
$$
with respect to a suitably chosen basis determined by the line.
Why the family of lines is $X_{{2,4}}$? Thank you very much.
geometry algebraic-geometry representation-theory schubert-calculus
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
$endgroup$
I am reading the file. I have a question on pae 18. It is said that: Given a line in $mathbb{R}^3$, the family of lines intersecting it can be interpreted in $G(2, 4)$ as the Schubert variety
$$
X_{{2,4}}=overline{left(begin{matrix}
* & 1 & 0 & 0 \
* & 0 & * & 1
end{matrix}right)}
$$
with respect to a suitably chosen basis determined by the line.
Why the family of lines is $X_{{2,4}}$? Thank you very much.
geometry algebraic-geometry representation-theory schubert-calculus
geometry algebraic-geometry representation-theory schubert-calculus
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
edited Dec 28 '18 at 11:00
Matt Samuel
39.2k63870
39.2k63870
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
asked Aug 12 '15 at 6:54
LJRLJR
6,66641850
6,66641850
$begingroup$
I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15
add a comment |
$begingroup$
I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15
$begingroup$
I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15
$begingroup$
I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15
add a comment |
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I have exactly the same question. Thanks for asking!
$endgroup$
– nekodesu
Jun 19 '18 at 15:15