The Rising Sea: Foundations of Algebraic Geometry Notes

math.stanford.edu

41 points·ibobev··7 comments

What makes this 850 page document "notes"? How large would a non-"notes" version be?

For the easily intimidated, here are smaller introductions:

https://www.math.purdue.edu/~arapura/graph/algcurve.html

https://www.math.purdue.edu/~arapura/preprints/algeom.pdf

“Notes” is short for “lecture notes” and has nothing to do with size.

The current version is more "textbook" than "notes", but like many textbooks it originated as lecture notes because no sane person would sit down and write a textbook.

FOAG is probably the shortest readable introduction to serious algebraic geometry anyone has written. That's the nature of algebraic geometry.

CHAPTER 27 The twenty-seven lines on a cubic surface

"You are now ready to be initiated into the secret fellowship of the twenty-seven lines."

Gotta understand abstract algebra and probably topology first.

Actually slightly more than that. A college level abstract algebra class is unlikely to cover much of commutative algebra. You'll want to know a fair amount of Module Theory for this book. Reading through the classic Atiyah MacDonald book should be more than enough.

A module is the "same" thing as a vector space (that we all know and love), except the underlying scalars are ring, instead of field (i.e. no division, e.g. integers). So it's like linear algebra when your scalars are stuff like integers or polynomials.

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