What is...the Riemann-Roch theorem?

Опубликовано: 30 Март 2026
на канале: VisualMath

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Goal.
I would like to tell you a bit about my favorite theorems, ideas or concepts in mathematics and why I like them so much.

This time.
What is...the Riemann-Roch theorem? Or: Allowing poles.

Disclaimer.
Nobody is perfect, and I might have said something silly. If there is any doubt, then please check the references.

Slides.
http://www.dtubbenhauer.com/youtube.html

TeX files for the presentation.
https://github.com/dtubbenhauer/My-Te...

Thumbnail.
https://en.wikipedia.org/wiki/Holomor...

Main discussion.
https://en.wikipedia.org/wiki/Riemann...
https://web.ma.utexas.edu/users/grego...
https://en.wikipedia.org/wiki/Holomor...
https://en.wikipedia.org/wiki/Meromor...
https://en.wikipedia.org/wiki/Maximum...

Background material.
https://en.wikipedia.org/wiki/Complex...
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Differe...
https://en.wikipedia.org/wiki/Polynomial
https://en.wikipedia.org/wiki/Rationa...
https://en.wikipedia.org/wiki/Power_s...
https://en.wikipedia.org/wiki/Smoothness
https://en.wikipedia.org/wiki/Taylor_...
https://en.wikipedia.org/wiki/Riemann...
https://en.wikipedia.org/wiki/Genus_(...)

Computer talk.
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...
https://reference.wolfram.com/languag...

Pictures used.
https://en.wikipedia.org/wiki/File:Co...
https://en.wikipedia.org/wiki/Holomor...
https://en.wikipedia.org/wiki/Maximum...
https://en.wikipedia.org/wiki/Zeros_a...
Again https://en.wikipedia.org/wiki/Zeros_a...
https://en.wikipedia.org/wiki/Riemann...

YouTube and co.
   • Riemann Roch  (Introduction)
   • The Riemann-Roch Theorem for Surfaces
   • Riemann Roch: structure of genus 1 curves

#geometry
#analysis
#mathematics