A projective algebraic variety (over an algebraically closed field ) is the 0-locus of a homogeneous ideal of polynomials in variables over in the projective n-space .
The archetypical example is projective space itself. In direct generalization of this but less evident: every Grassmannian is naturally a projective variety, even a smooth variety.
This generalizes to quiver representations. Every Grassmannian of a Quiver representation is a projective variety. In fact, every projective variety arises this way (Reineke, ‘12).
Last revised on September 27, 2020 at 15:09:47. See the history of this page for a list of all contributions to it.