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A variety is a class of algebras that is closed under homomorphisms, subalgebras, and direct products. Examples include the variety of groups, the variety of rings, the ...

An algebraic variety is a generalization to n dimensions of algebraic curves. More technically, an algebraic variety is a reduced scheme of finite type over a field K. An ...

An Abelian variety which is canonically attached to an algebraic variety which is the solution to a certain universal problem. The Albanese variety is dual to the Picard ...

Let V be a variety, and write G(V) for the set of divisors, G_l(V) for the set of divisors linearly equivalent to 0, and G_a(V) for the group of divisors algebraically equal ...

An Abelian variety is an algebraic group which is a complete algebraic variety. An Abelian variety of dimension 1 is an elliptic curve.

An affine variety V is an algebraic variety contained in affine space. For example, {(x,y,z):x^2+y^2-z^2=0} (1) is the cone, and {(x,y,z):x^2+y^2-z^2=0,ax+by+cz=0} (2) is a ...

An algebraic variety is called irreducible if it cannot be written as the union of nonempty algebraic varieties. For example, the set of solutions to xy=0 is reducible ...

A class of subvarieties of the Grassmannian G(n,m,K). Given m integers 1<=a_1<...<a_m<=n, the Schubert variety Omega(a_1,...,a_m) is the set of points of G(n,m,K) ...

Let m_1, m_2, ..., m_n be distinct primitive elements of a two-dimensional lattice M such that det(m_i,m_(i+1))>0 for i=1, ..., n-1. Each collection Gamma={m_1,m_2,...,m_n} ...

The set C_(n,m,d) of all m-D varieties of degree d in an n-dimensional projective space P^n into an M-D projective space P^M.