(undergrad) Algebraic Geometry Textbook Recommendations
Bix - Conics and also Cubics is possibly one of the most obtainable. I assume a senior high school pupil that did the BC calculus curriculum can read this and also get a whole lot out of it. Yet I would certainly concur with the others concerning Cox, Little, O'Shea - Ideals Varieties and also Algorithms being the 'ideal' undergraduate message.
See the MathOverflow inquiry concerning specifically this : Best Algebraic Geometry text book?
Personally, from what little bit I've seen,
Everyone is connecting to that MO inquiry, so permit me to link to an additional MO question which is extra pertinent to this details demand.
Additionally, I need to state that it partly relies on what you are seeking. Should this be for self research with little aid from teachers? After that your best choice would certainly be to adhere to Ravi Vakil's course next semester or utilize his old notes here.
If you plan on having a teacher over see the self research after that I assume that Ueno's books : Alg Geom 1 and 2, which I assume are wonderful for self research. (I need to state that his lower degree book is not virtually as excellent and also I would certainly NOT advise it.) An additional solid prospect for led self research would certainly be Harris' nice intro.
If you are mosting likely to supply a training course or take a training course after that I assume everybody's buddy would certainly behave increased by this masterpiece would certainly be a pleasant training course, yet likely also tough for basic.
I assume that covers the essentials. :D
EDIT : Two even more remarks, this publication is irritating and also I do not assume it is ideal to consider for basics attempting to find out algebraic geometry, specifically if they are relocating to modern-day scheme concept. And also an additional publication with a really various sensation, yet an actually enjoyable means to start thinking of algebraic geometry is Katz' Enumerative Geometry book. It was created specifically for basics, and also covers some actually cool product that can offer some excellent inspiration to think of algebraic geometry and also geography.
Cox, Little, and also O'Shea is a superb publication. I would certainly additionally such as to advise Miles Reid's Undergraduate Algebraic Geometry, which unlike Hartshorne or several various other typical referrals was created especially with undergrads in mind. You need to additionally look into his publication on commutative algebra ; I located both really informing.