Timeline for Are there any known criteria for quadratic mapping from R^n to R^n being surjective?
Current License: CC BY-SA 3.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2016 at 13:33 | answer | added | Qwerty | timeline score: 1 | |
| Jan 13, 2014 at 17:07 | answer | added | Name | timeline score: 0 | |
| Jan 9, 2014 at 11:29 | answer | added | Alex Degtyarev | timeline score: 2 | |
| Jan 4, 2014 at 10:44 | answer | added | David Wehlau | timeline score: 1 | |
| Jan 3, 2014 at 18:42 | comment | added | Alex Degtyarev | Sorry, my bad. Regarded as $Rp^n\to Rp^n$, your maps already are non-generic as needed. I remove my comment. | |
| Jan 3, 2014 at 17:25 | comment | added | JHM | I must admit that i don't believe your claim that quadratic maps are `almost never surjective'. They seem to as stable as "sets of open cones covering R^n". But, I am also unclear on whether or not we can expect a typical quadratic map $Q=(q_1, \ldots, q_n)$ to have the origin as an isolated solution to $Q=0$ or to have $d(\sum q_i^2)$ vanish only at the origin? | |
| Jan 3, 2014 at 17:08 | comment | added | JHM | @AlexDegtyarev: Could you be so generous as to elaborate in the form of an answer. I am unclear why the pull-back is quadric, why I must hope for degeneration, and what is a `double' hyperplane? | |
| Jan 2, 2014 at 22:54 | comment | added | Alex Degtyarev | Criterion in terms of what? Foe $n=2$, there is a classification; it may serve as a source for further guessing: Alex Degtyarev. Quadratic transformations Rp2 --> Rp2. In: Topology of Real Algebraic Varieties and Related Topics, Amer. Math. Soc. Transl. (2), 173 (1996), 61-73. | |
| Jan 2, 2014 at 20:30 | comment | added | JHM | Nice question. But the two posted `answers' are really very far from answers and -- in my opinion -- should be deleted. | |
| Jan 2, 2014 at 14:05 | comment | added | Rampant_mouse | The problem is linked to representation theory via invariant theory. | |
| Dec 31, 2013 at 14:58 | comment | added | Douglas Zare | What is the connection with representation theory? | |
| Dec 31, 2013 at 13:25 | answer | added | joro | timeline score: 5 | |
| Dec 31, 2013 at 12:04 | history | edited | Pietro Majer | CC BY-SA 3.0 |
added 26 characters in body
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| Dec 31, 2013 at 8:59 | answer | added | Glasby | timeline score: 6 | |
| Dec 31, 2013 at 6:20 | review | First posts | |||
| Dec 31, 2013 at 6:50 | |||||
| Dec 31, 2013 at 6:01 | history | asked | Rampant_mouse | CC BY-SA 3.0 |