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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.

If K is a finite complex and h:|K|->|K| is a continuous map, then Lambda(h)=sum(-1)^pTr(h_*,H_p(K)/T_p(K)) is the Lefschetz number of the map h.

The commutation operation [a,b]=ab-ba corresponding to the Lie product.

The multiplication operation corresponding to the Lie bracket.

A simplicial complex K is said to be locally finite if each vertex of K belongs only to finitely many simplices of K.

The Maclaurin-Bézout theorem says that two curves of degree n intersect in n^2 points, so two cubics intersect in nine points. This means that n(n+3)/2 points do not always ...

Any cubic curve that passes through eight of the nine intersections of two given cubic curves automatically passes through the ninth.

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

An algebraic surface of degree eight. The maximum number of ordinary double points known to exist on an octic surface is 168 (the Endraß octics), although the rigorous upper ...

A curve obtained by fitting polynomials to each ordinate of an ordered sequence of points. The above plots show polynomial curves where the order of the fitting polynomial ...