What are...ringed spaces?
Goal.
Explaining basic concepts in the intersection of geometry and algebra in an intuitive way.
This time.
What are...ringed spaces? Or: Enter, morphisms!
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.
Warning.
There is a typo on one of the slides, an f^(-1) should be a \phi^(-1), see the comments.
Slides.
http://www.dtubbenhauer.com/youtube.html
Website with exercises.
http://www.dtubbenhauer.com/lecture-a...
Thumbnail.
Picture from the first video slides.
Classical algebraic geometry.
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Commuta...
https://en.wikipedia.org/wiki/Multiva...
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Affine_...
https://en.wikipedia.org/wiki/Project...
https://en.wikipedia.org/wiki/Quasi-p...
https://en.wikipedia.org/wiki/Line_(g...)
https://en.wikipedia.org/wiki/Circle
https://en.wikipedia.org/wiki/Parabola
https://en.wikipedia.org/wiki/Ellipse
https://en.wikipedia.org/wiki/Hyperbola
https://en.wikipedia.org/wiki/Cubic_p...
https://en.wikipedia.org/wiki/Ellipti...
Modern algebraic geometry.
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Scheme_...)
https://en.wikipedia.org/wiki/Formal_...
https://en.wikipedia.org/wiki/Ind-scheme
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Algebra...
Modern algebraic geometry version 2.
https://en.wikipedia.org/wiki/Algebra...
https://en.wikipedia.org/wiki/Gr%C3%B...
https://en.wikipedia.org/wiki/Cylindr...
https://en.wikipedia.org/wiki/Tropica...
Applications of (algebraic) geometry.
https://math.stackexchange.com/questi...
Pictures used.
https://upload.wikimedia.org/wikipedi...
https://www.wikidata.org/wiki/Q168344...
A modification of https://i.sstatic.net/NEzWK.png
https://mathinsight.org/media/image/i...
Picture created using https://reference.wolfram.com/languag...
Some books I am using (I sometimes steal some pictures from there).
https://agag-gathmann.math.rptu.de/cl...
https://www.cambridge.org/core/books/...
https://bertini.nd.edu/book.html
https://mathoverflow.net/questions/24...
Computer talk.
https://magma.maths.usyd.edu.au/magma...
https://reference.wolfram.com/languag...
#algebraicgeometry
#geometry
#mathematics