Algebraic variety

The affine plane curve y2 = x3 - x. The corresponding projective curve is called an elliptic curve.

Algebraic varieties are the central objects of study in algebraic geometry. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.

单词	Projective algebraic set
释义	Projective algebraic set 英语百科 Algebraic variety Algebraic varieties are the central objects of study in algebraic geometry. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers. Modern definitions generalize this concept in several different ways, while attempting to preserve the geometric intuition behind the original definition.
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Projective algebraic set

Algebraic variety