Timeline for Geometric meaning of coherent sheaves $\mathcal{F} \otimes \mathcal{O}_{\mathbb{P}^n}(d)$ over $\mathbb{P}^n$
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Jun 16, 2021 at 15:30 | comment | added | Donu Arapura | @gigi I guess these would be of the generated by the Euler vector field $\sum x_i\partial/\partial x_i$. | |
| Jun 16, 2021 at 15:23 | comment | added | gigi | I think that by Euler sequence $$0 \rightarrow \mathcal{O}_{\mathbb{P}^n}(-1) \rightarrow \mathcal{O}_{\mathbb{P}^n}^{n+1} \rightarrow \mathcal{T} \rightarrow 0$$ after taking the twist by $\mathcal{O}(d)$ you have to take into the account the Kernel coming from $\mathcal{O}_{\mathbb{P}^n}(d-1) \rightarrow \mathcal{O}(d)_{\mathbb{P}^n}^{n+1}$ that will be a $\binom{n+d-1}{n}$ dimensional vector space of relations among the homogenenous polynomials $(f_0,\dots,f_n)$. Do you know how to express these relations and what they mean? | |
| Jun 16, 2021 at 15:05 | history | answered | Donu Arapura | CC BY-SA 4.0 |