Timeline for vector bundles over projective line over an affine line
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 12, 2019 at 20:58 | comment | added | prochet | The point is precisely that I don't want to modify the $\mathbb{A}^{1}$-factor. | |
| Dec 12, 2019 at 20:12 | comment | added | Piotr Achinger | Re: @prochet's follow-up question. I doubt it, but an argument would have to be of global nature. There are moduli spaces of semistable reflexive sheaves on $\mathbb{P}^n$, and not all of these sheaves are locally free for $n>1$; if you take a curve $C$ in the moduli space whose intersection with the non-locally free locus is a finite set $S$, then your question with $C\setminus S$ instead of $\mathbb{A}^1$ will likely have a negative answer. But it is not obvious how to ensure $C\setminus S \simeq \mathbb{A}^1$. | |
| Dec 12, 2019 at 14:43 | comment | added | Minseon Shin | I don't know, and I would also like to know. | |
| Dec 12, 2019 at 13:44 | comment | added | prochet | and does it also hold for vector bundles over $\mathbb{P}^{n}\times\mathbb{A}^{1}$? | |
| Dec 12, 2019 at 11:46 | history | answered | Minseon Shin | CC BY-SA 4.0 |