Geometry of The Function Field
If V is a variety over a field K, then the function field K(V) is a field extension of the ground field K over which V is defined; its transcendence degree is equal to the dimension of the variety. All extensions of K that are finitely-generated as fields arise in this way from some algebraic variety.
Properties of the variety V that depend only on the function field are studied in birational geometry.
Read more about this topic: Function Field Of An Algebraic Variety
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