I am a graduate student with good mathematical maturity (I took advanced courses like category theory, commutative algebra...). I want to study algebraic geometry from Mumford's red book. I find it difficult to keep motivated. Is there any class notes supplements Mumford?
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asked Jul 29, 2015 at 10:39
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2$\begingroup$ Maybe you would find some more examples motivating, such as are found in Harris's introductory book Algebraic Geometry, or Igor Dolghachev's free book on classical algebraic geometry, available on his website: math.lsa.umich.edu/~idolga/CAG.pdf Fulton's Algebraic Curves is also free now I think, math.lsa.umich.edu/~wfulton/CurveBook.pdf and there is the fascinating old book by Semple and Roth. $\endgroup$– roy smithCommented Jul 29, 2015 at 14:10
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$\begingroup$ [PDF]Solutions to Hartshorne's Algebraic Geometry - WordPress ... divisibility.files.wordpress.com/2013/.../…... Solutions to Hartshorne's Algebraic Geometry. Andrew Egbert. October 3, 2013. $\endgroup$– Al-AmraniCommented Jul 30, 2015 at 22:38
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$\begingroup$ Hartshorne'book is an excellent classical graduate ref. in Algebraic Geometry. It is not free but it contains plenty of exercises the solutions of which are free ! (see above). $\endgroup$– Al-AmraniCommented Jul 30, 2015 at 22:45
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$\begingroup$ I’m in a (¿similar?) position. I find Miles Reid’s stuff more concrete (UAG, OPV, Fano 3-folds, …). I also liked Knörrer and Brieskorn’s book which begins with a lot of actual drawings (with history!) of specific curves. If you look at Stillwell, Brieskorn, Hirzebruch, Reid, you will see overlaps. The Simons Foundation interviewed Brieskorn; this video could be a start. Fulton helps too. Plus 3264 and all that. I’m someone for whom consulting 3–10 sources in parallel is somehow easier than 1 (like balancing a stool on one leg). $\endgroup$– isomorphismesCommented Jan 24, 2020 at 18:57
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1 Answer
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You could have a look at Vakil's "Foundations of algebraic geometry" ? [Available on his Stanford homepage]
Eisenbud&Harris' "Geometry of schemes" is quite good to get the points too (pun intended)
answered Jul 29, 2015 at 11:21
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1$\begingroup$ Vakil is great, but definitely need presence of motivation. $\endgroup$ Commented Jul 30, 2015 at 14:06
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2$\begingroup$ Learning anything seriously needs presence and motivation! The only thing you can gain by acting like a vegetable is weight :-P $\endgroup$ Commented Aug 1, 2015 at 14:23