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The study of Algebraic Curves, Algebraic Varieties, and
their generalization to 
-D.
See also Algebraic Curve, Algebraic Variety, Commutative Algebra, Differential Geometry, Geometry, Plane Curve, Space Curve
References
Abhyankar, S. S.  Algebraic Geometry for Scientists and Engineers.  Providence, RI: Amer. Math. Soc., 1990.
 
Cox, D.; Little, J.; and O'Shea, D.  Ideals, Varieties, and Algorithms: An Introduction to 
  Algebraic Geometry and Commutative Algebra, 2nd ed.  New York: Springer-Verlag, 1996.
 
Eisenbud, D.  Commutative Algebra with a View Toward Algebraic Geometry.  New York: Springer-Verlag, 1995.
 
Griffiths, P. and Harris, J.  Principles of Algebraic Geometry.  New York: Wiley, 1978.
 
Hartshorne, R.  Algebraic Geometry, rev. ed.  New York: Springer-Verlag, 1997.
 
Lang, S.  Introduction to Algebraic Geometry.  New York: Interscience, 1958.
 
Pedoe, D. and Hodge, W. V.  Methods of Algebraic Geometry, Vol. 1.  Cambridge, England: Cambridge University Press, 1994.
 
Pedoe, D. and Hodge, W. V.  Methods of Algebraic Geometry, Vol. 2.  Cambridge, England: Cambridge University Press, 1994.
 
Pedoe, D. and Hodge, W. V.  Methods of Algebraic Geometry, Vol. 3.  Cambridge, England: Cambridge University Press, 1994.
 
Seidenberg, A. (Ed.).  Studies in Algebraic Geometry.  Washington, DC: Math. Assoc. Amer., 1980.
 
Weil, A.  Foundations of Algebraic Geometry, enl. ed.  Providence, RI: Amer. Math. Soc., 1962.