Timeline for Under which conditions on the homogeneous ideal $ I $, the quotient ring $ \mathbb{C} [X_0, \dots, X_n]/I $ is a regular ring?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 23, 2018 at 7:47 | comment | added | Zach Teitler | @YoYo: Yes. If $I$ is generated by linear forms $\ell_i$ then generators of $I^{\text{lin}}$ include $\ell_i^{\text{lin}} = \ell_i$. Conversely $I^{\text{lin}}$ is generated by linear forms by definition, so if $I = I^{\text{lin}}$ then $I$ is generated by linear forms, too. | |
| Sep 9, 2018 at 20:33 | comment | added | YoYo | Please, is $I$ homogeneous, generated by linear forms if and only if : $I = I^{ \mathrm{lin} } = \{ \ \text{ the ideal generated by the linear terms } f^{ \mathrm{lin} } \text{ of all } f \in I \ \} $ such that : $ f^{ \mathrm{lin} } $ is the linear term of $f$ as the degree one homogeneous polynomial in its expression as a sum of homogeneous polynomials in the variables $x_i$ 's ? Thank you . | |
| Sep 8, 2018 at 0:58 | vote | accept | YoYo | ||
| Sep 7, 2018 at 6:23 | history | answered | Zach Teitler | CC BY-SA 4.0 |