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How I Learned to Love Algebraic Geometry

johncarlosbaez.wordpress.com

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Re: How I Learned to Love Algebraic Geometry

#51

Post by johncarlosbaez »

chmaynard wrote: post #17
melling wrote: post #12

Joan Baez’s dad, his uncle, gave him the physics book that he wrote. Hopefully, someday when we see Joan Baez represented in movies, we’ll see her physicist father, perhaps giving a physics book to his 8 year old nephew.

In 1968, I enjoyed taking a physics course at Harvard Summer School that was taught by Dr. Albert Baez. He had a home in Cambridge and graciously invited the entire class over for a party after the course ended. The highlight of the evening was an impromptu performance by his daughter Joan.

Cool! It sounds fun. Back then she used to sing at the so-called Nameless Coffeehouse in Harvard. Unfortunately I was 7 years old in 1968, so I missed all this.

Re: How I Learned to Love Algebraic Geometry

#52

Post by johncarlosbaez »

maaaats wrote: post #11

What are some good resources for grasping or learning more about algebraic geometry?

My favorite intros to algebraic geometry are these:

Igor R. Shafarevich, Basic Algebraic Geometry, two volumes, third edition, Springer, 2013.

Phillip Griffiths and Joseph Harris, Principles of Algebraic Geometry, 1994. (Especially nice if you like complex analysis, differential geometry and de Rham theory.)

David Eisenbud and Joseph Harris, The Geometry of Schemes, Springer, 2010. Currently at https://www.maths.ed.ac.uk/~v1ranick/papers/eisenbudharris.p...

But whenever I want to learn some new field of math I start with Wikipedia. This is a pretty good overview:

https://en.wikipedia.org/wiki/Algebraic_geometry

Re: How I Learned to Love Algebraic Geometry

#53

Post by johncarlosbaez »

Grustaf wrote: post #42
throwawaymath wrote: post #20

Earlier quoted context omitted.

This isn't a fun answer, but you basically can't without substantial background in undergrad mathematics. The subject has some of the highest prerequisites of any upper undergrad/lower grad level math course, as it touches on (and uses) just about everything you'd learn through an undergrad math degree. I don't want to discourage you, I'm just being realistic. If you want to work towards algebraic geometry, you can c…

Everyone should also read Modern Geometry book by Dubrovin, Novikov and Fomenko, it starts pretty basic and covers a lot of ground, and is extremely well written.

That book is great, but not mainly about algebraic geometry: it's more about differential geometry.

Re: How I Learned to Love Algebraic Geometry

#54

Post by johncarlosbaez »

selimthegrim wrote: post #50
melling wrote: post #12

Joan Baez’s dad, his uncle, gave him the physics book that he wrote. Hopefully, someday when we see Joan Baez represented in movies, we’ll see her physicist father, perhaps giving a physics book to his 8 year old nephew.

He’s written several. Me and my grad student colleagues found “Gauge fields, knots and gravity” to be very accessible

I wrote "Gauge Fields, Knots and Gravity", but we were talking about my uncle, who wrote "The New College Physics: a Spiral Approach".

Re: How I Learned to Love Algebraic Geometry

#55

Post by Grustaf »

johncarlosbaez wrote: post #53
Grustaf wrote: post #42

Earlier quoted context omitted.

Everyone should also read Modern Geometry book by Dubrovin, Novikov and Fomenko, it starts pretty basic and covers a lot of ground, and is extremely well written.

That book is great, but not mainly about algebraic geometry: it's more about differential geometry.

I know, but itäs an excellent introduction to geometry in general, like some of the other books listed. It’s probably not even possible to get from 0 to algebraic geometry in a single book...

Re: How I Learned to Love Algebraic Geometry

#56

Post by selimthegrim »

johncarlosbaez wrote: post #54
selimthegrim wrote: post #50

Earlier quoted context omitted.

He’s written several. Me and my grad student colleagues found “Gauge fields, knots and gravity” to be very accessible

I wrote "Gauge Fields, Knots and Gravity", but we were talking about my uncle, who wrote "The New College Physics: a Spiral Approach".

Oh sorry, I thought they were talking about you too
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