On self-associated sets of points in small projective spaces

2006/04/24 by Ivan Petrakiev, Petrakiev, Ivan · 1 citation
Mathematics · #13H10 #14N05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Finite Group Theory Research #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0604518

openalex publication_date 2006/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study moduli of ``self-associated'' sets of points in \bf Pⁿ for small n. In particular, we show that for n=5 a general such set arises as a hyperplane section of the Lagrangean Grassmanian LG(5,10) ⊂ \bf P¹⁵ (this was conjectured by Eisenbud-Popescu in \it Geometry of the Gale transform, J. Algebra 230); for n=6, a general such set arises as a hyperplane section of the Grassmanian G(2,6) ⊂ \bf P¹⁴. We also make a conjecture for the next case n=7. Our results are analogues of Mukai's characterization of general canonically embedded curves in \bf P⁶ and \bf P⁷, resp.

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• The Self-Projecting Grassmannian

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