algebraic variety

(redirected from Projective varieties)

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 ?
Zhang, Building blocks of polarized endomorphisms of normal projective varieties, Adv.
1078 174184 Free resolutions of coordinate rings of projective varieties and related topics (Kyoto 1998).
Lectures on curves, surfaces and projective varieties; a classical view of algebraic geometry.
Mezzetti, Linear congruences and systems of conservation laws, Projective Varieties with Unexpected Properties (A Volume in Memory of Giuseppe Veronese.
Bialynicki-Birula, On fixed points of torus actions on projective varieties, Bull.
Sols: Moduli space of principal sheaves over projective varieties, Ann.
Appendices are included on projective varieties and complex manifolds, homology and cohomology, and vector bundles and Chern classes.
The first of two volumes of proceedings from the July 2015 pure mathematics summer institute presents 22 papers on such topics as wall-crossing implies Brill-Noether: applications of stability conditions on surfaces, syzygies of projective varieties of large degree: recent progress and open problems, enumerative geometry and geometric representation theory, Frobenius techniques in birational geometry, singular Hermitian metrics and the positivity of direct images of pluri-canonical bundles, and non-commutative deformations and Donaldson-Thomas invariants.
(For the definition of the MRC-fibration, see, e.g., [12, Theorem 2.3 and Definition 2.4].) Then there exist smooth projective varieties Y and B, a birational morphism [pi] : Y [right arrow] X and a surjective morphism with connected fibers f : Y [right arrow] B such that B is not uniruled and the fiber of f is rationally connected.
Rational Points, Rational Curves, and Entire Holomorphic Curves on Projective Varieties; proceedings
In this paper curves and surfaces are understood to be complex projective varieties, and we are interchanging the use of a divisor and its associated line bundle.