Birational geometry

curve obtained by intersecting a cone and a plane

field of algebraic geometry that seeks to determine when two algebraic varieties are birationally equivalent (isomorphic outside lower-dimensional subsets)

in algebraic geometry, a transformation on an algebraic variety or scheme, wherein a closed subvariety is replaced with the space of lines passing through it (in the case of a point, a projective space), commonly used to resolve singularities

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

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

a surface birationally equivalent to the projective plane ; rational variety of dimension two

mathematical system

algorithm in algebraic geometry

concept in algebraic geometry

the group of birational automorphisms of the n-dimensional projective space over a field k

branch of birational geometry aiming to construct the simplest birational model of a projective variety