Schubert Cell Structure for some variety with prescribed bilinear form
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We know the construction of Schubert cell complex structure for the case of Grassmann manifold $Gr_k(mathbb{C}^n)$ i.e variety of all k- dimensional subspaces $V$ of $mathbb{C}^n$.
Consider that there is bilinear form B on $mathbb{C}^n$. How to give a Schubert cell structure on the set of all V, k- dimensional subspaces of $mathbb{C}^n$ such that B restricted on V is nonsingular.
Thank you in advance. Any help will be appreciated.
bilinear-form cw-complexes schubert-calculus
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
$endgroup$
add a comment |
$begingroup$
We know the construction of Schubert cell complex structure for the case of Grassmann manifold $Gr_k(mathbb{C}^n)$ i.e variety of all k- dimensional subspaces $V$ of $mathbb{C}^n$.
Consider that there is bilinear form B on $mathbb{C}^n$. How to give a Schubert cell structure on the set of all V, k- dimensional subspaces of $mathbb{C}^n$ such that B restricted on V is nonsingular.
Thank you in advance. Any help will be appreciated.
bilinear-form cw-complexes schubert-calculus
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
$endgroup$
$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01
add a comment |
$begingroup$
We know the construction of Schubert cell complex structure for the case of Grassmann manifold $Gr_k(mathbb{C}^n)$ i.e variety of all k- dimensional subspaces $V$ of $mathbb{C}^n$.
Consider that there is bilinear form B on $mathbb{C}^n$. How to give a Schubert cell structure on the set of all V, k- dimensional subspaces of $mathbb{C}^n$ such that B restricted on V is nonsingular.
Thank you in advance. Any help will be appreciated.
bilinear-form cw-complexes schubert-calculus
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
$endgroup$
We know the construction of Schubert cell complex structure for the case of Grassmann manifold $Gr_k(mathbb{C}^n)$ i.e variety of all k- dimensional subspaces $V$ of $mathbb{C}^n$.
Consider that there is bilinear form B on $mathbb{C}^n$. How to give a Schubert cell structure on the set of all V, k- dimensional subspaces of $mathbb{C}^n$ such that B restricted on V is nonsingular.
Thank you in advance. Any help will be appreciated.
bilinear-form cw-complexes schubert-calculus
bilinear-form cw-complexes schubert-calculus
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
asked Dec 27 '18 at 22:28
SurojitSurojit
393110
393110
$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01
add a comment |
$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01
$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01
add a comment |
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$begingroup$
Do you mean nondegenerate?
$endgroup$
– Matt Samuel
Dec 28 '18 at 11:43
$begingroup$
@MattSamuel: Yes. I mean nondegenerate.
$endgroup$
– Surojit
Dec 28 '18 at 17:55
$begingroup$
@MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine.
$endgroup$
– Surojit
Jan 2 at 20:00
$begingroup$
I wasn't confident it was correct. If you want I can undelete it
$endgroup$
– Matt Samuel
Jan 2 at 20:01