BAG1.1. Toric Varieties 1 - Affine Varieties over C

Edit: Not quite a typo at 4:45: for the V function, we have V(I n J)=V(I) u V(J). The vanishing points are unchanged if we replace V(I n J) with V(IJ), but if you get into the scheme game, there's a difference. See links in the comments.

Basic Algebraic Geometry: We define affine varieties over the complex numbers, the Zariski topology on C^n, and the Zariski closure of a subset X in C^n.

Prerequisites: A first year of graduate algebra, but the course was run with advanced undergraduates in mind. Chapter 0 forthcoming, which will give a better idea of the big picture.

[arkapointer]

Greetings from India.
Very concise and to the point video.
Please continue the series and make videos on Commutative Algebra and Homology theory.

[chandrapandey]

Wow these lectures are surprisingly easy to grasp for a good graduate student....

[danielplacido]

Thank you, this was the best video I found on affine varieties. Was there a typo at entrance (2) on 4:45 on the Zariski's topology? isn't the variety of the union the variety of the product instead? V(I)UV(J) = V(IJ)

[orbital]

5:55 "There are not nearly as many polynomials as there are continuous functions on C^n."

Technically, both sets have cardinality 2^Aleph_0 (cardinality of the continuum) so there's actually just as many polynomials as there are continuous functions.

[MrGatward]

I really appreciate how succinctly you are teaching this material. I have been looking for introductory videos in algebraic geometry for some time now so please continue the series! Do you think you will be lecturing on sheaf theory eventually?

[Grassmpl]

You're an expert in every branch of mathematics. Is there any math you dont know?

[cheeckjerokee]

Are there any associated exercises to accompany these lectures? Thank you so much for these videos by the way! I'm reviewing Group Theory and Point Set Topology as well as learning a bit of Algebraic Geometry and Representation Theory.

[spikeeleslie]

Bob, can you explain to me what a "generating set" is? or can you link me to a video explaining this?

[EvaSlash]

Hey Dr. Bob! What are your opinions on the field of statistics? One of my teachers once told me that math majors hate statistics, why is that?