Algebraic varieties

ratio of polynomial functions

mathematical object studied in the field of algebraic geometry

coarse topology defined on algebraic varieties and schemes

function whose logarithmic derivative is a generating function for the number of solutions of a set of equations defined over a finite field

subfield of K(X) is isomorphic to K(X)

theorem

point of an algebraic variety without a defined tangent space

algebraic variety defined within a projective space

field extension that contains an element algebraically independent from the base field

type of algebraic variety

the space of lines in a complex vector space

algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety, which can be combinatorially encoded via systems of cones (“fans”) or polytopes

algebraic variety over a field K birationally equivalent to a projective space of some dimension over K

closed immersion from a product of projective spaces (of dimension m and n) to a projective space (of dimension mn+m+n)

basic birational invariant

algebraic variety defined within an affine space

function between varieties that is given locally by polynomials

the field of ratios of polynomial functions on a variety

type of algebraic variety

the top exterior power of the cotangent bundle of a nonsingular algebraic variety

homogeneous polynomial of degree 3