# Schubert Cell Structure for some variety with prescribed bilinear form

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.

• Do you mean nondegenerate? – Matt Samuel Dec 28 '18 at 11:43
• @MattSamuel: Yes. I mean nondegenerate. – Surojit Dec 28 '18 at 17:55
• @MattSamuel: Dear Sir, what happened to the answer? Is there any problem with that answer? I guess that was fine. – Surojit Jan 2 at 20:00
• I wasn't confident it was correct. If you want I can undelete it – Matt Samuel Jan 2 at 20:01