I am curious as to why in algebraic and differential geometry so much special attention is given to curves and surfaces in contras to higher dimensional manifolds or varieties. I would like to know if there are deep mathematical reasons for this or if it is just due to the practical fact that we humans live in a $3$-dimensional space and thus these seem the natural objects to study from a practical point of view. I wonder if there is something mathematical going on or it is just arbitrary because I believe that there should be much more richness in higher dimensions but I am not sure about it. Thanks a lot and sorry if the question is not appropriate or too broad.
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