Category
page 1Birational geometry
conic section
curve obtained by intersecting a cone and a plane
birational geometry
field of algebraic geometry that seeks to determine when two algebraic varieties are birationally equivalent (isomorphic outside lower-dimensional subsets)
blowing up
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
Lüroth's theorem
subfield of K(X) is isomorphic to K(X)
rational variety
algebraic variety over a field K birationally equivalent to a projective space of some dimension over K
rational surface
a surface birationally equivalent to the projective plane ; rational variety of dimension two
Enriques–Kodaira classification
mathematical system
Cox–Zucker machine
algorithm in algebraic geometry
Kodaira dimension
concept in algebraic geometry
rational normal curve
Cremona group
the group of birational automorphisms of the n-dimensional projective space over a field k
birational invariant
minimal model program
branch of birational geometry aiming to construct the simplest birational model of a projective variety