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Let Gamma be an algebraic curve in a projective space of dimension n, and let p be the prime ideal defining Gamma, and let chi(p,m) be the number of linearly independent ...

A homology class in a singular homology theory is represented by a finite linear combination of geometric subobjects with zero boundary. Such a linear combination is ...

A generalization of an ordinary two-dimensional surface embedded in three-dimensional space to an (n-1)-dimensional surface embedded in n-dimensional space. A hypersurface is ...

The dimension d of any irreducible representation of a group G must be a divisor of the index of each maximal normal Abelian subgroup of G. Note that while Itô's theorem was ...

The length is the longest dimension of an object.

The ring of integers of a number field K, denoted O_K, is the set of algebraic integers in K, which is a ring of dimension d over Z, where d is the extension degree of K over ...

A measure for which the q-dimension D_q varies with q.

The Pontryagin number is defined in terms of the Pontryagin class of a manifold as follows. For any collection of Pontryagin classes such that their cup product has the same ...

Given a vector space V, its projectivization P(V), sometimes written P(V-0), is the set of equivalence classes x∼lambdax for any lambda!=0 in V-0. For example, complex ...

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...