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.

  • $\begingroup$ 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

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