Timeline for Can you ``perturb'' a submanifold to intersect transversally with any other smooth submanifold of projective space?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2011 at 15:56 | comment | added | Tom Goodwillie | Yes, that's right. | |
| Oct 25, 2011 at 13:22 | comment | added | Ritwik | One further thing. Requiring $\pi_{\mathcal{D}}$ to be a submersion is a sufficient criteria, but not a necessary one. I simply need $\pi_{\mathcal{D}}$ to be transverse to $X$ (which is guaranteed if it is a submersion). | |
| Oct 25, 2011 at 11:10 | comment | added | Tom Goodwillie | Yes, I believe so. | |
| Oct 25, 2011 at 2:48 | comment | added | Ritwik | I have edited the question slightly. According to your argument, the answer to my question should now be yes, since $\pi_{D}$ is a submersion. Am I correct? | |
| Oct 22, 2011 at 0:04 | comment | added | Tom Goodwillie | I did not express myself very well. I meant that $X$ is parametrized by pairs $q=(x_0,y_0)$, and that for any given point $q$ the manifold $H_q$ fails to be transverse to $X$ (where it meets $X$, namely at the point in $X$ corresponding to $q$). Does that make sense? | |
| Oct 21, 2011 at 19:08 | comment | added | Ritwik | Thank you for the answer. But I have a question about the counter example. Here your X also depends on the point q. So as you change q, both the X and the H move. In my question, X does not depend on q. As you change q only H should change. X should remain fixed. So do you still think this is a counter example to my question? | |
| Oct 21, 2011 at 18:59 | vote | accept | Ritwik | ||
| Oct 21, 2011 at 15:39 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |