Timeline for Finding the dimension of the intersection of two real algebraic varieties
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 11, 2020 at 10:05 | answer | added | Liviu Nicolaescu | timeline score: 3 | |
| Jul 11, 2020 at 9:40 | comment | added | Liviu Nicolaescu | For a postive integer $n$ denote by $P_n$ the vector space of polynomials of degree $\leq n$ in three variables. Sard's theorem shows that if $n$ is sufficiently large, there exists a measure zero subset $Z\subset P_n\times P_n$ such that for $(p,q)\in P_n\times P_n\setminus Z$ the set $\{p=q=0\}$ has dimension $1$ if nonempty. In fact $Z$ itself is semialgebraic. | |
| Jul 10, 2020 at 22:33 | comment | added | Dima Pasechnik | because you work over the reals, parameter counting will tell you nothing. | |
| S Jul 10, 2020 at 21:38 | history | suggested | Rodrigo de Azevedo | CC BY-SA 4.0 |
Added higher-order tag. Minor edits.
|
| Jul 10, 2020 at 21:12 | review | Suggested edits | |||
| S Jul 10, 2020 at 21:38 | |||||
| Jul 10, 2020 at 21:11 | comment | added | Rodrigo de Azevedo | What exactly is a polynomial in $\mathbb{R}^3$? Do you mean in $\mathbb{R} [x_1, x_2, x_3]$? | |
| Jul 10, 2020 at 19:55 | review | First posts | |||
| Jul 10, 2020 at 21:26 | |||||
| Jul 10, 2020 at 19:53 | history | asked | mathuser | CC BY-SA 4.0 |