Algebraic Geometry
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2004.
52323 pgs.

Algebraic Geometry
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2004
Algebraic Geometry
Encyclopedia article; The Columbia Encyclopedia, Sixth Edition, 2004
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ALGEBRAIC GEOMETRY branch of
geometry, based on
analytic geometry, that is concerned with geometric objects (loci) defined by algebraic relations among their coordinates (see
Cartesian coordinates). In plane geometry an algebraic curve is the locus of all points satisfying the
polynomial equation f(x,y)=0; in three dimensions the polynomial equation f(x,y,z)=0 defines an algebraic surface. In general, points in n-space are defined by ordered sequences of numbers (x1,x2,x3,…xn), where each n-tuple specifies a unique point and x1, x2, x3,…xn are members of a given
field (e.g., the complex numbers). An algebraic hypersurface is the locus of all such points satisfying the polynomial equation f(x1,x2,x3,…xn)=0, whose coefficients are also chosen from the given field. The intersection of two or more algebraic hypersurfaces defines an algebraic set, or variety, a concept of particular importance in algebraic geometry. ____________________The Columbia Encyclopedia, Sixth Edition Copyright© 2004, Columbia University Press. Licensed from Lernout & Hauspie Speech Products N.V. All rights reserved. -1326- | |
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Publication Information: Encyclopedia Article Title: Algebraic Geometry. Encyclopedia Title: The Columbia Encyclopedia, Sixth Edition. Publisher: Columbia University Press. Place of Publication: New York. Publication Year: 2004.
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