The Two Lives of the Grassmannian
arXiv:2401.03684
Abstract
The real Grassmannian is both a projective variety (via Plücker coordinates) and an affine variety (via orthogonal projections). We connect these two representations, and we develop the commutative algebra of the latter variety. We introduce the squared Grassmannian, and we study applications to determinantal point processes in statistics.
arXiv comment19 pages. Theorem 3.8 and Remark 5.11 are new