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.
References in periodicals archive ?
Let S be a smooth projective rational surface and [phi] : S [right arrow] [P.sup.1] a fibration whose general fibre F is a projective curve of genus g [greater than or equal to] 1.
Table 1 lists the results of our numerical procedure for the projective curve corresponding to f(x, y) = 0 in Example 1.
of Notre Dame, Indiana), and Ulrich (Purdue U., Indiana) investigate the singularities of a rational projective curve by studying a Hilbert-Burch matrix for the row vector [g1,.
a smooth and irreducible projective curve defined over C, and let g be its genus.
(0.3) [Mathematical Expression Omitted] for M in [Mathematical Expression Omitted] for a projective curve Y/[F.sub.q] and a smooth [Q.sub.l]-sheaf M on Y.
Let C be a smooth, projective curve over an algebraically closed field k of genus g(C) [greater than or equal to] 2.
Coppens, The singular locus of the secant varieties of a smooth projective curve, Arch.
The Igusa curve [X.sub.n] of level [p.sup.n] is defined to be the unique smooth projective curve over k which contains [X.sub.n[.sup.o]] as a dense open subvariety.
Let C be a smooth projective curve of genus g > 2 over an algebraically closed filed k.
Let k be a two dimensional local field of characteristic zero and X be a smooth projective curve defined over k.
Let C be a smooth complex projective curve of genus g [is greater than or equal to] 2 embedded in a projective space [P.sup.r] by a very ample line bundle N of degree d.