What is...the Jacobi criterion?

Goal.
Explaining basic concepts in the intersection of geometry and algebra in an intuitive way.

This time.
What is...the Jacobi criterion? Or: Rank of a matrix.

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

Disclaimer.
In this course I try to cover my favorite topics in algebraic geometry, from classical ideas such as algebraic varieties, to modern ideas such as schemes, to really modern ideas such as tropical varieties. I give a very biased collection of topics, and not nearly all that can be said will be addressed. Sorry for that.

Slides.

Website with exercises.

Thumbnail.
Picture from the first video slides.

Classical algebraic geometry.

Modern algebraic geometry.

Modern algebraic geometry version 2.

Applications of (algebraic) geometry.

Pictures used.
A picture created by ChatGPT
Another picture created by ChatGPT
Yes another picture created by ChatGPT
Picture from the previous video

Some books I am using (I sometimes steal some pictures from there).

Computer talk.

#algebraicgeometry
#geometry
#mathematics