projective variety
algebraic variety defined within a projective space
Scorza variety
smooth projective variety, of maximal dimension among those whose k–1 secant varieties are not the whole of projective space
abelian variety
projective abelian algebraic group
projective space
space of 1-dimensional linear subspaces (lines passing through the origin) in a vector space
weighted projective space
Proj construction applied to a polynomial ring where the generators have been assigned arbitrary positive-integer degrees
Mori dream space
geometric projective variety