Rational Functions and Rational Maps
Let X ⊂ A n be an irreducible affine variety. Since its coordinate ring A(X) is an integral domain, we can form its quotient field; this is called the rational function field of X and is usually denoted K(X); its elements are called rational functions on X. Note that if Y ⊂ X is an open subset that is an affine variety in its own right (as in the discussion on page 19), the function field of Y will be the same as that of X.
KeywordsOpen Subset Projective Variety Inverse Image Exceptional Divisor Blow Down
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