MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $V$ be an n-dimensional complex vector space, and $u\in S^nV$ be a polynomial, $G(u)$ be the stabilizer of $u$ in $GL(V)$. Let $[v]\in\overline{GL(V)\cdot[u]}\subset\mathbb{P}(S^nV)$, but $v\notin End(V)\cdot [u]$, and $GL(V)\cdot [v]$ is of codimension $1$ in $\overline{GL(V)\cdot [u]}$, where $\overline{GL(V)\cdot [u]}$ means the closure of $GL(V)$-orbit of $[u]$ in $\mathbb{P}S^nV$. Here $\overline{GL(V)\cdot [u]}$ need not be normal. Obviously $\dim G(v)=\dim G(u)+1$, I just wonder what the precise relationship with $G(u)$ and $G(v)$ is. Thanks a lot!

share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.