Timeline for When is the space of holomorphic sections of the tensor product of two line bundles given by the span of the tensor product of the basis?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2018 at 17:39 | comment | added | Ritwik | @Sandor: I understand now. | |
| Jun 11, 2018 at 16:25 | comment | added | Sándor Kovács | @Ritwik: I didn't say that very ample is enough. I said that very ample and giving a projectively normal embedding is. | |
| Jun 10, 2018 at 19:35 | comment | added | abx | No, definitely not. For a simple example, take a curve $C$ of genus $g\geq 4$ and a general line bundle $L$ on $C$ of degree $g+3$. Then it is standard to prove that the linear system $|L|$ embeds $C$ into $\mathbb{P}^3$. But $h^0(L^2)= g+7$ is greater than $\dim \mathsf{S}^2H^0(L)=10$. | |
| Jun 10, 2018 at 18:14 | comment | added | Ritwik | I actually meant to say Very Ample (i.e. the Kodiara map from S to P(H^0(L)^dual) is an embedding ). Are you saying that the statement is true when L is very ample (as opposed to just ample)? | |
| Jun 10, 2018 at 17:42 | history | answered | Sándor Kovács | CC BY-SA 4.0 |