Timeline for Cohomology of the tangent sheaf of $\mathbb{P}(1,2,3)$
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 11, 2014 at 19:56 | vote | accept | Puzzled | ||
| Feb 11, 2014 at 19:09 | comment | added | Jason Starr | Just to add one comment: away from small characteristic (2 and 3), the computation "should" be the same whether you work with $\mathbb{P}(1,2,3)$ as a stack or as a coarse moduli space. There is an action of $\mathbb{G}_m$ on $\mathbb{A}^3\setminus\{0\}$, and the affine, geometric quotient $q:(\mathbb{A}^3\setminus\{0\})\to \mathbb{P}(1,2,3)$ gives a way of realizing $\Theta$ as the invariant part of $q_* \widetilde{T}$, for $\widetilde{T}$ defined as Sasha suggests on $\mathbb{A}^3\setminus\{0\}$. Since $q$ is affine, compute for $\widetilde{T}$ and take $\mathbb{G}_m$-invariants. | |
| Feb 11, 2014 at 19:05 | history | answered | Sasha | CC BY-SA 3.0 |