Algebraic geometry 1 Introduction

This lecture is part of an online algebraic geometry course (Berkeley math 256A fall 2020), based on chapter I of "Algebraic geometry" by Hartshorne. The full set of lectures is in the playlist "Algebraic geometry I: varieties".

(The course continues in the playlist "Algebraic geometry II: schemes" based on chapter II.)

The first lecture describes a birational map from a circle to a line.

[riadsouissi]

glad someone of the caliber of this field prize medalist is posting YouTube videos on subjects explained in a rather accessible manner!

[vatsalyavaibhavsrivastava]

I am blessed and lucky to have found these lectures. Thanks!

[rhealastname]

"Is kind of stupid, because..." That's the best part of the video because for a brief second he sounds like he's just complaining about some inside joke. Love it.

[runggp]

really appreciate the uploading and sharing the wonderful lectures with the public! Hope more deep and systematic lectures on these advanced topics can be created and shared! really awesome great

[prakashpanangaden]

These lectures are remarkable for their lucidity.

[ipudisciple]

Small typo at 3:00. You say (and mean) (r^2+s^2)/2 but write (r^2+s)/2.

[matsnordstrom]

Thank you ever so kindly, professor. This is some of the best content I've seen on the internet so far. And with "some of ", I mean "".

[sivanzou]

This is pretty cool!!! I got stuck in reading Milne‘s notes and cannot understand the motivation of doing algebraic geometry. Now I believed that my question will be answered.

[luciusirving]

I might get into algebraic geometry after calculus.

[Pawn-Sac]

The correspondence he refers to is every point on the y-axis (0, t) corresponds to a unique point (x, y) on the circle. The point (-1, 0) is used to determine which two points go together: given (-1, 0) pick a point (x, y) and that determines (0, t). This is why (-1, 0) needs to be excluded from the correspondence: if I pick the point (-1, 0) for my (x, y) then the line is tangent to the circle. This wasn't immediately clear to me, so I imagine its not immediately clear to someone else.

[petergentoac]

This is such a great video. So good I've had to come back for another watch. Brilliant stuff!

[llcdraco]

Thanks a lot for your work and lectures! Love them!

[benzmanslamg]

Thanks for sharing these wonderful lectures.

[XingfengLin]

Hi, professor, I wonder if there is a book which your lectures are mainly based on. I just want to find such a book so that I can keep watching your lectures and learn well. THANK YOU!

[steevelevy]

THANKS YOU PROFESSOR BORCHEDS VERY GOOD COURSE. I AM A FRENCH STUDIENT BUT WITH SUBTITLE IT'S CLEAR

[sebastjansslavitis]

at the beginning how did you come to conclusion that x, y, z are coprime?

[juanitoperez]

Does anybody can recommend a book to study AG?

[mckdoeful]

at 1:39: "since they can't all be even, we see that z must be odd" -- why can't x and y both be odd, and z even?

[aron]

Can someone explain the (x+iy)(x-iy)=zz^-1=1 at 16:56? I don't think it adds up.

[imthebestmathematician]

In about 2:35 why is z+x and z-x are squares of two numbers?