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 ?
Murre, On a conjectural filtration on the Chow groups of an algebraic variety, parts I and II, Indag.
A Fano manifold X is a smooth projective algebraic variety with the ample first Chern class [c.sub.1](X) = - [K.sub.X].
The Hodge conjecture is a major unsolved problem in the field of algebraic geometry that relates the algebraic topology of a non-singular complex algebraic variety and the subvarieties of that variety.
Let P be a parabolic subgroup of G, i.e., a subgroup of G for which the quotient B/P is a projective algebraic variety; this condition is equivalent to P contains B.
In this context, a regulator is a map from the algebraic K-theory of an algebraic variety to a suitable cohomology theory such as etale cohomology or Deligne cohomology.
Put differently: The underlying manifold of an algebraic variety does not determine these invariants," he added.
It is the purpose of the present paper to investigate the structured distance of a real irreducible tridiagonal matrix to the algebraic variety of real normal irreducible tridiagonal matrices, which we denote by I.
Then there exists a proper algebraic variety V [subset] S st.
We start in Section 2 with the definition of the arc space of an algebraic variety as the set of formal power series solutions (in one variable) to the defining equations of the variety.
Russo, Some remarks on nef and good divisors on an algebraic variety, C.
For P in P(r, d), and E an r-filtered bundle on an algebraic variety (or algebraic scheme) X, by substituting the Chern roots of E for [x.sub.1], ..., [x.sub.n], ordering these roots so that [x.sub.[r.sub.[j.sup.+1]]], ..., [x.sub.[r.sub.j+1]] correspond to Chern roots of [E.sub.j]/[E.sub.j+1], we get a class denoted P(E); this is a class in the cohomology group [H.sup.2d](X; Q) if X is a complex variety, or in the Chow cohomology group [A.sup.d](X; Q) in general.