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 ?
A Fano manifold X is a smooth projective algebraic variety with the ample first Chern class [c.
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.
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.
Russo, Some remarks on nef and good divisors on an algebraic variety, C.
Russo, On the complement of a nef and big divisor on an algebraic variety, Math.
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.
Section 2 introduces notation used throughout the paper, section 3 presents an upper bound for the distance in the Frobenius norm of a real tridiagonal matrix to the algebraic variety of real normal tridiagonal matrices.
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.
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.
Finally, we outline (Section 6) an alternative interpretation of the higher critical groups as discrete analogues of the Chow groups of an algebraic variety.