algebraic variety

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algebraic variety

[‚al·jə‚brā·ik və′rī·əd·ē]
(mathematics)
A set of points in a vector space that satisfy each of a set of polynomial equations with coefficients in the underlying field of the vector space.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Then H is an affine curve in [N.sup.1.sub.C](Y) [equivalent] [C.sup.2].
Then by Lemma 3.6, each affine line [L'.sub.n] is an irreducible component of the affine curve H.
Then [X.sub.n[.sup.o]] is a smooth affine curve over k.
Since [Y.sub.0[.sup.o]] is a smooth affine curve over k we may define Y0 to be the compactification of [Y.sub.0[.sup.o]].
As above [Y.sub.n[.sup.o]] is a smooth affine curve over k so we may define [Y.sub.n] to be the compactification of [Y.sub.n[.sup.o]] .For each n [greater than or equal to] there is a natural map from [Y.sub.n] to [X.sub.n] which makes [Y.sub.n] a branched cover of [X.sub.n] of degree