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<p>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.</p>

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The two lives of the Grassmannian

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年7月3日

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  • Karel Devriendt,
  • Hannah Friedman,
  • Bernhard Reinke,
  • Bernd Sturmfels

摘要

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.