I am a combinatorist by training and I am interested in learning about the connections between combinatorics and Schubert varieties. The theory of Schubert varieties seems to be a difficult area to break into if one has not already studied it in graduate school. I don't have a formal course in Algebraic Geometry, but I do know some Commutative Algebra. Does anyone have any recommendations on what Algebraic Geometry one needs to understand (and what books/papers one should read) in order to begin studying Schubert varieties? Algebraic Geometry is such a huge subject that I am trying to figure out what is essential to this particular study and what is not. Thanks, in advance, for any suggestions!
[Math] Learning About Schubert Varieties
ag.algebraic-geometryco.combinatorics
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Best Answer
I would suggest Part III of Fulton's Young Tableaux book (of which you should skip Part I) as the best starting point for learning about Schubert varieties.
One can get very far in this subject with a naive 19th century view of algebraic geometry, especially if one is willing to occasionally accept without proof a few foundational facts (for example the basics of intersection theory). I would suggest that you don't need to learn algebraic geometry in general for now, though if you're serious about working in this area you'll eventually need to get some feel for what kinds of questions algebraic geometers are interested in.