Complex algebraic variety information

{P} ^{n}} , is an algebraic variety. These are usually simply referred to as projective varieties. Let X be a complex algebraic variety. Then there is a...

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as...

concerned with the study of spaces such as complex manifolds and complex algebraic varieties, functions of several complex variables, and holomorphic constructions...

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective n-space P n {\displaystyle \mathbb {P}...

Algebraic variety - Roughly speaking, an (complex) analytic variety is a zero locus of a set of an (complex) analytic function, while an algebraic variety...

mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry...

in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

manifolds have very different flavors: compact complex manifolds are much closer to algebraic varieties than to differentiable manifolds. For example,...

unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties...

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials. It is also called...

In the mathematical field of algebraic geometry, a singular point of an algebraic variety V is a point P that is 'special' (so, singular), in the geometric...

mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the...

are purely algebraic and rely on commutative algebra. Some are restricted to algebraic varieties while others apply also to any algebraic set. Some are...

In algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field k of some family of polynomials in the...

In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic...

theory to all complex algebraic varieties, not necessarily smooth or compact. Namely, the cohomology of any complex algebraic variety has a more general...

In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre...

In algebraic geometry, a Fano variety, introduced by Gino Fano in (Fano 1934, 1942), is an algebraic variety that generalizes certain aspects of complete...

mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has...

mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of...

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles. It is the connected...

algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety...

generally, an algebraic curve is an algebraic variety of dimension one. (In some contexts, an algebraic set of dimension one is also called an algebraic curve...

In mathematics, complex dimension usually refers to the dimension of a complex manifold or a complex algebraic variety. These are spaces in which the local...

Hodge class is a particular kind of homology class defined on a complex algebraic variety V, or more generally on a Kähler manifold. A homology class x...

mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety X, such that for any variety Y the projection morphism...

universal algebra, an algebraic structure is called an algebra; this term may be ambiguous, since, in other contexts, an algebra is an algebraic structure...

In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the...