Serre duality

So today, in Regensburg, at our student seminar on Riemann surfaces, I gave a wonderful talk on Serre duality. It was a rather long talk (80 minutes), we had to prepare some sort of detailed handouts for people and we were actually supposed to prove things rigorously. I had already given one such a talk on simplicial topology earlier this semester and it went very well, so, at least, the format seemed to be suitable for me.

I think I managed just fine. It is difficult to give a long proof in such a limited time (at least for me), especially if you need to build up all the theory beforehand. The book my talk was based on is the "Lectures on Riemann surfaces" by O. Forster, in which the proof is, to my taste, rather convoluted and unmotivated. And, admittedly, too long to present in public. And except for the last five minutes of the proof, in which I had to use a certain diagram for one sheaf and then, in reality, used a different one,  I am quite confident that I could give people more than just the book.

Moreover, I used a slightly different approach than the book, because I could not afford the luxury of the clean, uninterrupted, yet unmotivated exposition. I put a great emphasis on how the various objects I defined will be used in the proof or why we care. Unfortunately, the audience was traditionally ranging from dispassionate to impassive and had it not been for the experience gained for me and some details falling into place in my mind as I spoke, I would have preferred to spend my afternoon differently.

For those of you interested in my impression of the Serre duality, here is a link to my notes (beware of the last part, which is a bit inaccurate and I relied more on my hand-written comments from my own perusal of the proof)
https://www.dropbox.com/s/2frsw8ywxm3xl79/Serre_duality.pdf?dl=0

And bonus points to those who correctly identified which meaning of perusal I used there.

Regensburg yesterday.