Reference for Algebraic Geometry

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manpreet Tuteehub forum best answer Best Answer 3 years ago

 

I tried to learn Algbraic Geometry through some texts, but by Commutative Algebra, I left the subject; many books give definitions and theorems in Commutative algebra, but do not explain why it is needed.

Can one suggest a good reference to learn this subject geometrically, which would also give ways to translate geometric ideas in algebraic manner, possibly through examples?

Particularly, I am interested in differentials on algebraic curves, Riemann-Roch theorem, various definitions of genus and their equivalences, and mainly groups related to complex algebraic curves such as group of automorphisms, monodromy group etc.

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