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A generalization to a quartic three-dimensional surface is the quartic surface of revolution (x^4-ax^3)+a^2(y^2+z^2)=0, (1) illustrated above. With a=1, this surface is ...

A technical conjecture which connects algebraic K-theory to étale cohomology. The conjecture was made more precise by Dwyer and Friedlander (1982). Thomason (1985) ...

A quintic surface is an algebraic surface of degree 5. Togliatti (1940, 1949) showed that quintic surfaces having 31 ordinary double points exist, although he did not ...

A K-rational point is a point (X,Y) on an algebraic curve f(X,Y)=0, where X and Y are in a field K. For example, rational point in the field Q of ordinary rational numbers is ...

An algebraic surface which can be represented implicitly by a polynomial of degree six in x, y, and z. Examples of quartic surfaces include the Barth sextic, Boy surface, ...

In algebraic topology, a p-skeleton is a simplicial subcomplex of K that is the collection of all simplices of K of dimension at most p, denoted K^((p)). The graph obtained ...

A transcendental number is a (possibly complex) number that is not the root of any integer polynomial, meaning that it is not an algebraic number of any degree. Every real ...

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

If X is any space, then there is a CW-complex Y and a map f:Y->X inducing isomorphisms on all homotopy, homology, and cohomology groups.

If P(x) is an irreducible cubic polynomial all of whose roots are real, then to obtain them by radicals, you must take roots of nonreal numbers at some point.