Timeline for Applications of isotropic quadratic forms
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 15, 2016 at 22:22 | comment | added | Dima Pasechnik | Isotropic forms are easy and fun to deal with over finite fields. And you might connect the particular case of $U_4(\mathbb{F}_2)$ to 27 lines on cubic surfaces... | |
| Dec 15, 2016 at 21:02 | answer | added | Noam D. Elkies | timeline score: 1 | |
| Dec 15, 2016 at 20:33 | history | edited | LSpice |
Added tag
|
|
| Dec 15, 2016 at 19:43 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Dec 15, 2016 at 19:43 | comment | added | Todd Trimble | Made CW according to the OP's wishes (people are encouraged to tweak or extend or correct it). | |
| Dec 15, 2016 at 19:31 | answer | added | Will Jagy | timeline score: 4 | |
| Dec 15, 2016 at 18:26 | comment | added | Noam D. Elkies | also (and possibly more suitable for undergraduates) the determinant of a 2-by-2 matrix, and trace(A^2) for square matrices of any order, are natural quadratic forms that represent zero. And a conic plane curve is basically a quadratic form in 3 real variables that represents zero (up to multiplying the form by a nonzero scalar). If it has rational coefficients then the existence of rational points is equivalent to the question of whether the form represents zero nontrivially over the rationals. | |
| Dec 15, 2016 at 18:24 | comment | added | Noam D. Elkies | "Isotropic" = forms that represent zero? Sure; they often arise as intersection forms on algebraic surfaces (e.g. an elliptic fibration yields a nontrivial divisor with self-intersection zero), and are often useful to describe the structure of positive-definite forms (quite a few examples in Conway and Sloane's "SPLAG" = *Sphere Packings, Lattices, and Groups"). | |
| Dec 15, 2016 at 18:12 | history | asked | Jean Raimbault | CC BY-SA 3.0 |