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A visiting student a few weeks ago was talking to another student about some mathematics that I had never heard of before and I wrote down something that he wrote on the board.

$$f(z)=1, L=\mathcal{O},\qquad f(z)=z,L=\mathcal{O}(1),\qquad f(z)=z^2,L=\mathcal{O}(2)$$

Where can I read more about this? Sorry if this is vague, it's vague precisely because it is vague to me what this is. I believe these are related to complex line bundles, but I cannot find this $\mathcal{O}$ notation.

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    $\begingroup$ The first $L$ is just the trivial bundle. For each pairs, one might think of $f$ as a section of $L$, where $L$ are lne bundles on $\mathbb P^1$. $\endgroup$ – user99914 Nov 26 '16 at 10:50
  • $\begingroup$ @JohnMa Do you know a book leaning towards algebraic geometry that covers this sort of content? I have looked at vector bundles before, and projective space, but haven't come across this in an algebraic geometry book. $\endgroup$ – Jason Nov 26 '16 at 11:03
  • $\begingroup$ (Or any book for that matter, of course) $\endgroup$ – Jason Nov 26 '16 at 11:36
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Daniel Huybrechts : Complex Geometry - An Introduction

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  • $\begingroup$ Thanks, this does seem to cover it! $\endgroup$ – Jason Nov 27 '16 at 4:16
  • $\begingroup$ You're welcome! $\endgroup$ – paf Nov 27 '16 at 12:27

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