If I have a symmetrical bilinear form and a projective variety. How do I restrict that form to my variety?
Let's say I'm studying a hyper-quadric.
I get its singular, and I want to classify it.
It occurred to me, as I obtained two planes, to cut with another plane that did not contain any point of the singular, because if there was a cut they had to be real (it was in $P_3(\mathbb{R})$) and if not, they are complex.
But I don't remember how to restrict one vector variety to another.
Thanks