The Two Lives of the Grassmannian
Algebraic Geometry
2024-07-08 v3 Combinatorics
Optimization and Control
Abstract
The real Grassmannian is both a projective variety (via Pl\"ucker 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.
Keywords
Cite
@article{arxiv.2401.03684,
title = {The Two Lives of the Grassmannian},
author = {Karel Devriendt and Hannah Friedman and Bernhard Reinke and Bernd Sturmfels},
journal= {arXiv preprint arXiv:2401.03684},
year = {2024}
}
Comments
19 pages. Theorem 3.8 and Remark 5.11 are new