Timeline for Which projective varieties cannot appear as an exceptional divisor of a blow-up of the projective space
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 29, 2021 at 6:30 | comment | added | Francesco Polizzi | btw, in my last comment "unirational" should be "uniruled". | |
| Jun 27, 2021 at 15:34 | vote | accept | Ron | ||
| Jun 27, 2021 at 9:46 | comment | added | Francesco Polizzi | Ok, I wrote a short answer | |
| Jun 27, 2021 at 9:45 | answer | added | Francesco Polizzi | timeline score: 6 | |
| Jun 27, 2021 at 9:28 | comment | added | Ron | @FrancescoPolizzi Thanks. You could write your comments as the answer. This does answer my question to a large extent. | |
| Jun 27, 2021 at 9:25 | comment | added | Francesco Polizzi | unirational, but not rational in general. If you blow-up a smooth curve $C$ of genus $g\geq 1$ in $\mathbb{P}^3$, the exceptional divisor is a $\mathbb{P}^1$-bundle over $C$, that is not rational because it has irregularity $g$. | |
| Jun 27, 2021 at 9:20 | comment | added | Ron | @FrancescoPolizzi By your argument that it is the Proj of a normal sheaf, can't we further say that the irreducible components of the exceptional divisor must be rational? | |
| Jun 26, 2021 at 18:45 | comment | added | Francesco Polizzi | Is not the exceptional divisor always covered by rational curves (because it is the Proj of the normal sheaf)? This should exclude all the non-uniruled varieties, I think. | |
| Jun 26, 2021 at 18:21 | history | asked | Ron | CC BY-SA 4.0 |