Timeline for blow-up of $\mathbb{P}^5$ as a projective bundle
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 26, 2014 at 5:48 | comment | added | Cinzia Casagrande | It is easy to see what happens to toric divisors, but it is more difficult to study a general divisor in the linear system $|p^*\mathcal{O}(1,1,1)|$. If $H'_1\subset X'$ is the pull-back of $\{pt\}\times\mathbb{P}^1\times\mathbb{P}^1$, the transform $H_1$ of $H_1'$ in $X$ is the transform of a hyperplane in $\mathbb{P}^5$ containing 2 of the blown-up lines. Similarly you can consider in $X$ the transforms $H_2$ and $H_3$ of hyperplanes in $\mathbb{P}^5$ containing the 2 other pairs of blown-up lines. Then $\mathcal{O}_X(-H_1-H_2-H_3)$ corresponds to $p^*\mathcal{O}(-1,-1,-1)$. | |
| Apr 25, 2014 at 17:50 | comment | added | Libli | May I ask you another question? On $X'$ there is the line bundle $p^*\mathcal{O}(-1,-1,-1)$, where $p : X' \rightarrow \mathbb{P}^1 \times \mathbb{P}^1 \times \mathbb{P}^1$ is the canonical projection. Do you have an idea what is its transform when we flop it to $X$? | |
| Apr 25, 2014 at 8:45 | comment | added | Libli | That's a great answer! Thanks so much! | |
| Apr 25, 2014 at 8:44 | vote | accept | Libli | ||
| Apr 24, 2014 at 21:56 | review | First posts | |||
| Apr 24, 2014 at 22:08 | |||||
| Apr 24, 2014 at 21:32 | history | answered | Cinzia Casagrande | CC BY-SA 3.0 |