Timeline for How do I find the algebra representing the projective bundle of a direct sum of line bundles over a projective space?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 6, 2017 at 21:09 | comment | added | 54321user | For all of the downvoters, can you please explain why you gave me these votes? It seems like many Hartshorne level questions go above math.stackexchange and are more appropriately written here. | |
| Apr 14, 2017 at 22:35 | vote | accept | 54321user | ||
| Feb 13, 2017 at 22:30 | history | edited | 54321user | CC BY-SA 3.0 |
updated question with potential answer
|
| Feb 13, 2017 at 20:41 | vote | accept | 54321user | ||
| Feb 13, 2017 at 20:42 | |||||
| Feb 13, 2017 at 5:53 | review | Close votes | |||
| Feb 13, 2017 at 13:38 | |||||
| Feb 13, 2017 at 3:29 | answer | added | Sándor Kovács | timeline score: 8 | |
| Feb 13, 2017 at 2:58 | comment | added | 54321user | Yes, exactly. Sorry I did not put that into the question. | |
| Feb 13, 2017 at 2:47 | comment | added | Sándor Kovács | Aha, so your question is that you want an absolute Proj and not a relative Proj? | |
| Feb 13, 2017 at 2:43 | comment | added | 54321user | Sure, there is a hirzebruch surface $\mathbb{P}(\mathcal{O}\oplus\mathcal{O}(n)) = \text{Proj}(\mathbb{C}[s,t][x,y,z]/(s^ny - t^nz))$ from mathoverflow.net/questions/122952/on-a-hirzebruch-surface, but I am not sure how to find such an algebra in general. | |
| Feb 13, 2017 at 2:22 | comment | added | Sándor Kovács | But this is projective, so it will not be a Spec and I gave you a presentation as a Proj. I still don't understand what it is that you want. Could you give a projective example? | |
| Feb 13, 2017 at 1:35 | comment | added | 54321user | For example, $\text{Spec}(\text{Sym}(I/I^2))$ for $I = (xy,xz) \subset \mathbb{C}[x,y,z] = R$ is the scheme $\text{Spec}(R[a,b]/(az-by))$ | |
| Feb 13, 2017 at 1:27 | comment | added | Sándor Kovács | What do you mean by that? | |
| Feb 13, 2017 at 0:52 | comment | added | 54321user | No, I want to get an actual algebra presentation for this construction. | |
| Feb 13, 2017 at 0:48 | comment | added | Sándor Kovács | For any locally free sheaf $\mathscr E$, $\mathbb P(\mathscr E)=\mathrm {Proj}\ \mathrm{Sym} (\mathscr E)$. Is this what you are asking? | |
| Feb 13, 2017 at 0:25 | history | asked | 54321user | CC BY-SA 3.0 |