The Self-Projecting Grassmannian

2025/11/26 by Alheydis Geiger, Geiger, Alheydis, Francesca Zaffalon +1
Computer Science · Mathematics · #05-04 #05B35 #05E14 #14H10 #14Q99 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2511.21442

openalex publication_date 2025/11/26 · openalex created_date 2025/11/28 · openalex updated_date 2026/07/28

Abstract

We introduce the self-projecting Grassmannian, an irreducible subvariety of the Grassmannian parametrizing linear subspaces that satisfy a generalized self-duality condition. We study its relation to classical moduli spaces, such as the moduli spaces of pointed curves of genus g, as well as to other natural subvarieties of the Grassmannian. We further translate the self-projectivity condition in the combinatorial language of matroids, introducing self-projecting matroids, and we computationally investigate their realization spaces inside the self-projecting Grassmannian.

Citations

• Points on Rational Normal Curves and the ABCT Variety
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Related

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• The Grassmannian of affine subspaces
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• The Two Lives of the Grassmannian
• Baker--Bowler theory for Lagrangian Grassmannians