Timeline for Proj for rings graded by different things then $\mathbb N$ ?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 1, 2010 at 12:29 | vote | accept | Jan Weidner | ||
| Nov 29, 2010 at 16:20 | answer | added | J.C. Ottem | timeline score: 13 | |
| Nov 29, 2010 at 15:44 | comment | added | arsmath | Proj isn't just the grading. You also have to decide what corresponds to the the irrelevant ideal. | |
| Nov 29, 2010 at 15:36 | answer | added | Allen Knutson | timeline score: 8 | |
| Nov 29, 2010 at 15:12 | comment | added | Daniel Loughran | I think that using different gradings as you suggest corresponds to entering the realm of geometric invariant theory. Note that an $\mathbb{Z}$ grading on a ring is the same as an action of the multiplicative group $\mathbb{G}_m$. | |
| Nov 29, 2010 at 15:10 | comment | added | Qiaochu Yuan | An action of the multiplicative group on an affine variety induces a decomposition of its coordinate ring into irreps which are "polynomially defined," and this is where the N-grading comes from abstractly. So I guess one expects an action of a more general group to induce a grading by the corresponding polynomial irreps. | |
| Nov 29, 2010 at 14:53 | history | asked | Jan Weidner | CC BY-SA 2.5 |