Rational Functions and Rational Maps

  • Joe Harris
Part of the Graduate Texts in Mathematics book series (GTM, volume 133)


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.


Open Subset Projective Variety Inverse Image Exceptional Divisor Blow Down 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • Joe Harris
    • 1
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA

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