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A theorem that can be stated either in the language of abstract algebraic curves or transcendental extensions. For an abstract algebraic curve, if x and y are nonconstant ...

Relationships between the number of singularities of plane algebraic curves. Given a plane curve, m = n(n-1)-2delta-3kappa (1) n = m(m-1)-2tau-3iota (2) iota = ...

A subset of an algebraic variety which is itself a variety. Every variety is a subvariety of itself; other subvarieties are called proper subvarieties. A sphere of the ...

Two algebraic objects that are commutative, i.e., A and B such that A*B=B*A for some operation *, are said to commute with each other.

Given a subspace A of a space X and a map from A to a space Y, is it possible to extend that map to a map from X to Y?

A fiber space, depending on context, means either a fiber bundle or a fibration.

The canonical generator of the nonvanishing homology group on a topological manifold.

A curve and its polar reciprocal with regard to the fixed conic have the same Halphen transformation.

If f:(X,A)->(Y,B) is homotopic to g:(X,A)->(Y,B), then f_*:H_n(X,A)->H_n(Y,B) and g_*:H_n(X,A)->H_n(Y,B) are said to be the induced maps.

The simplicial complex formed from a family of objects by taking sets that have nonempty intersections.