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In algebraic geometry classification problems, an algebraic variety (or other appropriate space in other parts of geometry) whose points correspond to the equivalence classes ...

The spectrum of a ring is the set of proper prime ideals, Spec(R)={p:p is a prime ideal in R}. (1) The classical example is the spectrum of polynomial rings. For instance, ...

The Zariski topology is a topology that is well-suited for the study of polynomial equations in algebraic geometry, since a Zariski topology has many fewer open sets than in ...

The Grassmannian Gr(n,k) is the set of k-dimensional subspaces in an n-dimensional vector space. For example, the set of lines Gr(n+1,1) is projective space. The real ...

A group or other algebraic object is said to be Abelian (sometimes written in lower case, i.e., "abelian") if the law of commutativity always holds. The term is named after ...

Classical algebraic geometry is the study of algebraic varieties, both affine varieties in C^n and projective algebraic varieties in CP^n. The original motivation was to ...

A connection defined on a smooth algebraic variety defined over the complex numbers.

If R is a Noetherian ring, then S=R[X] is also a Noetherian ring.

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

The dilogarithm identity Li_2(-x)=-Li_2(x/(1+x))-1/2[ln(1+x)]^2.