algebraic variety
mathematical object studied in the field of algebraic geometry
toric variety
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 group
group that is an algebraic variety
affine variety
algebraic variety defined within an affine space
rational variety
algebraic variety over a field K birationally equivalent to a projective space of some dimension over K
projective variety
algebraic variety defined within a projective space
Line complex
3-dimensional family of lines in space
ruled variety
algebraic variety through every point on which is a straight line that lies on the variety
irreducible variety
type of algebraic variety
generalized flag variety
homogeneous space which is the quotient of a semisimple group by its parabolic subgroup
algebraic surface
algebraic variety of dimension two
algebraic curve
algebraic variety of dimension one
Klein quartic
compact Riemann surface of genus 3
arithmetic variety
quotient space of a Hermitian symmetric space by an arithmetic subgroup of the associated algebraic Lie group
complete variety
type of algebraic variety
Fake projective space
Complex algebraic variety
correspondence
binary relation between varieties defined by polynomials; a subvariety of the product of two varieties
quadric
locus of zeros of a quadratic polynomial (affine or projective, not necessarily real)
algebraic manifold
algebraic variety whose set of closed points naturally forms a manifold
Rational normal scroll
Algebraic geometry