Examples
The function field of a point over K is K.
The function field of the affine line over K is isomorphic to the field K(t) of rational functions in one variable. This is also the function field of the projective line.
Consider the affine plane curve defined by the equation . Its function field is the field K(x,y), generated by transcendental elements satisfying this algebraic relation.
Read more about this topic: Function Field Of An Algebraic Variety
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