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.

  • 1
    $\begingroup$ 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

Daniel Huybrechts : Complex Geometry - An Introduction

  • $\begingroup$ 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

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.