Algebraic geometry where to begin?

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Discussion Overview

The discussion revolves around recommendations for introductory resources in algebraic geometry, particularly in the context of its relevance to mathematical physics. Participants share their experiences with various texts and express their backgrounds in related mathematical fields.

Discussion Character

  • Exploratory
  • Technical explanation
  • Homework-related

Main Points Raised

  • One participant seeks recommendations for starting points in algebraic geometry, mentioning their background in topology, algebra, analysis, and other advanced mathematical topics.
  • Another participant suggests several texts, including "Basic Algebraic Geometry" by Shafarevich, "Algebraic Curves" by Fulton, and "Algebraic Geometry" by Hartshorne, noting their usefulness.
  • A participant expresses curiosity about the level of difficulty of Shafarevich's text, asking how elementary or advanced it is.
  • One contributor describes Shafarevich as starting fairly elementary but acknowledges that "elementary" is relative, and mentions that later chapters become more advanced.
  • Another participant notes that Hartshorne requires prior knowledge of commutative algebra, specifically referencing Eisenbud's work.
  • A suggestion is made to consider "Rings, Varieties, and Algorithms" by Cox, Little, and O'Shea as a companion text for real algebraic geometry.

Areas of Agreement / Disagreement

Participants generally agree on the usefulness of the recommended texts, but there is no consensus on the relative difficulty of these resources, as opinions vary on what constitutes "elementary" or "advanced."

Contextual Notes

Participants express varying levels of familiarity with the recommended texts, and there is an acknowledgment of the subjective nature of difficulty in mathematical literature.

Who May Find This Useful

Readers interested in algebraic geometry, particularly those with a background in mathematics or mathematical physics, may find the recommendations and discussions helpful.

styler
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Howdy folks,
I was wondering if anybody could recommend a good place to start learning algebraic geometry as might be relevant for current/recent mathematical physics.
I have opened Griffiths and Harris and found it sprawling ad frustruating.
For the sake of judging what might be appropriate, i am mainly interested in physics but i have completed stadarnd first year math course work in topology, algebra and analysis and additionally taken courses in functional analysis, differnetial topology, differetial geometry and alebraic topology...so i guess i "know" about what a very modest beginning third year grad student in math has learned.
Recomedations for several complex variables would be appreciated as well.
Any ideas?
Thanks in advance.
 
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Others suggested these texts for me:

Basic Algebraic Geometry - Shafarevich
Algebraic Curves - Fulton
Algebraic Geometry - Hartshorne

And I've found them useful so far. If you just wanted to look at one, I'd probably suggest Shafarevich.

Keep in mind that I've just started teaching myself the subject, so I'm by no means an expert on the available choices. :smile:
 
cool. thanks. I have heard about the first one...how elemetary/advanced is it?
 
It starts off, IMHO, fairly elementary. (admittedly, "elementary" is a relative term!) The later chapters go into schemes and are fairly more advanced, but Shafarevich is still nowhere near as difficult as Hartshorne. (I haven't peeked at the Complex Manifold chapters in Shafarevich, though)
 
hartshorne has as a precursor commutative algebra by eisenbud.

an intro alg. geometry book is rings varieties and algorithms by cox, little, and o'shea. it's prolly a good thing to have as a companion when looking at real alg. geometry.
 
thanks guys
maybe i'll post some questiogs as i go alog.
 

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