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The general curve of a system which is linearly dependent on a certain number of given irreducible curves will not have a singular point which is not fixed for all the curves ...

A transformation which is one-to-one and a surjection (i.e., "onto").

If two complementary Plücker characteristics are equal, then each characteristic is equal to its complement except in four cases where the sum of order and class is 9.

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

A bivector, also called a 2-vector, is an antisymmetric tensor of second rank (a.k.a. 2-form). For a bivector X^->, X^->=X_(ab)omega^a ^ omega^b, where ^ is the wedge product ...

For a smooth harmonic map u:M->N, where del is the gradient, Ric is the Ricci curvature tensor, and Riem is the Riemann tensor.

Every continuous map f:S^n->R^n must identify a pair of antipodal points.

The quartic with implicit equation x^4=x^2y-y^3. (1) The bow has vertical tangents at (+/-2/9sqrt(3),2/9) and horizontal tangents at (+/-1/4sqrt(2),1/4). Its curvature is ...

Let A_1, B_2, C_1, A_2, and B_1 be five points determining a conic. Then the conic is the locus of the point C_2=A_1(L·C_1A_2)·B_1(L·C_1B_2), where L is a line through the ...

An algebraic variety over a field K that becomes isomorphic to a projective space.