What is...the Segre embedding?

Goal.
Explaining basic concepts in the intersection of geometry and algebra in an intuitive way.
This time.
What is...the Segre embedding? Or: Multiplying polynomials? Kind of!
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.
www.dtubbenhaue...
Website with exercises.
www.dtubbenhaue...
Thumbnail.
Picture from the first video slides.
Classical algebraic geometry.
en.wikipedia.o...
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Modern algebraic geometry.
en.wikipedia.o...
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Modern algebraic geometry version 2.
en.wikipedia.o...
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Applications of (algebraic) geometry.
math.stackexch...
Pictures used.
Picture from • What are...(abstract) ...
images.saymedi...
i.sstatic.net/...
en.wikipedia.o...
i.ytimg.com/vi...
Some books I am using (I sometimes steal some pictures from there).
agag-gathmann....
www.cambridge....
bertini.nd.edu...
mathoverflow.n...
Computer talk.
magma.maths.us...
reference.wolf...
#algebraicgeometry
#geometry
#mathematics

[@guillem2601]

Hi Daniel, I just finished reading Andreas Gathmann alg geo notes from 2002 that you recomended me instead of reading Hartshorne. I have no words to thank you for recomending this, this is the first time I learn this much in such a short time.
But could you please spoil me what that image under the text "modern v2 alg. geo" in the thumbnail means?

[@VisualMath]

Great, I am glad that the book was helpful. I like it as well (and use it as the base for this video series) ☺
For me “modern v2” means either computational (yes, one can compute all of this with a machine) or tropical. Its a bit a matter of taste 😅