What is...the Cayley-Bacharach theorem?

Описание: 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 Cayley-Bacharach theorem? Or: Nine and nine!

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

Careful, potential misunderstanding.
As pointed out in the comments, “X points determine Y” should be “X points in generic position determine Y”. I forgot to say “in generic position” in the video, sorry for that.

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

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

Thumbnail.

Main discussion.
https://en.wikipedia.org/wiki/Cayley%...
https://en.wikipedia.org/wiki/Five_po...
https://www.ams.org/journals/bull/199...
https://arxiv.org/abs/math/0508076
https://en.wikipedia.org/wiki/Pappus%...
https://en.wikipedia.org/wiki/Pascal%...

Background material.
https://en.wikipedia.org/wiki/B%C3%A9...
https://en.wikipedia.org/wiki/Project...
https://en.wikipedia.org/wiki/Colline...
https://en.wikipedia.org/wiki/Cubic_p...
https://en.wikipedia.org/wiki/Project...
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Ellipti...
https://en.wikipedia.org/wiki/Riemann...

Computer talk.
https://doc.sagemath.org/pdf/en/refer...
https://doc.sagemath.org/html/en/refe...
https://ask.sagemath.org/question/491...

Pictures used.
https://upload.wikimedia.org/wikipedi...
https://qph.cf2.quoracdn.net/main-qim...
https://i.stack.imgur.com/3zk3v.png
https://elliotnoma.files.wordpress.co...
https://home.adelphi.edu/~stemkoski/E...
https://upload.wikimedia.org/wikipedi...
https://en.wikipedia.org/wiki/Cayley%...
https://en.wikipedia.org/wiki/Pappus%...
https://en.wikipedia.org/wiki/Pascal%...
Pictures created using https://reference.wolfram.com/languag...

YouTube and co.
   • Calculating the Cayley Bacharach Point  
   • Robert Lazarsfeld, Cayley-Bacharach theore...  
   • dotted gives me another cayley-bacharach geo  

#geometry
#algebra
#mathematics