What is...the identity theorem?
HTML-код
- Опубликовано: 3 окт 2024
- Goal.
Explaining basic concepts in the intersection of geometry and algebra in an intuitive way.
This time.
What is...the identity theorem? Or: Complex versus algebraic geometry.
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.
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Modern algebraic geometry.
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Modern algebraic geometry version 2.
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Applications of (algebraic) geometry.
math.stackexch...
Pictures used.
Picture created using reference.wolf...
upload.wikimed...
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More pictures created using reference.wolf...
A variation of the pictures above
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Picture created using reference.wolf...
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
1:30 But aha, I can rewind the video and have my mind blown now!
Haha, video technology for an infinite mind blow 🤣
truly a mind blowing theorem
I absolutely agree, in particular in tandem with its friend from complex analysis 😀
Serre’s GAGA, Chow’s theorem, and other comparison theorem makes the equivalences between complex analysis and algebraic geometry more precise.
By Chow’s theorem projective varieties are of interest. Holomorphic functions being infinitely complex-differential makes complex manifolds like Moishezon manifolds or smooth varieties of interest. Polynomials are holomorphic functions. Combining these ideas smooth projective varieties and related Chow motives are natural to consider when doing algebraic geometry.
I would even argue that most of the algebraic geometry that was discovered and developed in the 1930 to 1960 is motivated by complex analysis. I will make that a selling point of AG, we will see how that goes 😀
@@VisualMath I think complex analysis has motived algebraic geometry even earlier. For example, the Riemann-Roch theorem and its many generalizations considers poles, residues, and zeros of meromorphic functions on a compact Riemann surface (= elliptic curve over the complex numbers) or its corresponding generalization.
@@Jaylooker Ah, yes thanks, Riemann-Roch is actually a really good example 👍
@@VisualMath Yup 👍
Hi, really like your videos. The software you are using looks very very good, but then this software seems to have pallets to the left panel and above. I want to know what is this software you are using here. Hope you will let me know.
I think you are looking for this: xournalpp.github.io/
And thanks for the feedback, you are very welcome 😀