Timeline for relation between pull-back of Cartier divisors, invertible sheaves and global sections

4 events

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Sep 12, 2011 at 11:23	comment	added	Fei YE		By extension, I mean that each section $\mathcal{O}_X$ is the image of a section of $\mathcal{O}_{\mathbb{P}^n}$. In other words, a section of $\mathcal{O}_X$ is the restriction of a section of $\mathcal{O}_{\mathbb{P}^n}$ on $X$.
Sep 12, 2011 at 10:23	comment	added	user565739		@ Fei YE, could you explain why surjectivity implies that $D$ can be extended to a hyperplane in $\mathbb{P}^n$, this is just what I would like to know.
Sep 12, 2011 at 8:46	comment	added	Fei YE		Did you think about using the short exact sequence $0\to I_X(1)\to \mathcal{O}_{\mathbb{P}^n}(1)\to \mathcal{O}_X(1)\to 0$? Besides, the subjectivity $\Gamma(\mathcal{O}_{\mathbb{P}^n}(1))\to\Gamma( \mathcal{O}_X(1))$ tells us that $D$ can be extended to a hyperplane in $\mathbb{P}^n$.
Sep 11, 2011 at 21:56	history	asked	user565739	CC BY-SA 3.0