Affine and Projective Varieties

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


In this book we will be dealing with varieties over a field K, which we will take to be algebraically closed throughout. Algebraic geometry can certainly be done over arbitrary fields (or even more generally over rings), but not in so straightforward a fashion as we will do here; indeed, to work with varieties over nonalgebraically closed fields the best language to use is that of scheme theory. Classically, much of algebraic geometry was done over the complex numbers ℂ, and this remains the source of much of our geometric intuition; but where possible we will avoid assuming K = ℂ.


Projective Space Linear Subspace Projective Variety Quadratic Polynomial Affine Space 
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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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