On the codimension 1 PGL(3) orbit closures in Gr(3,6)

2025/07/24 by Tanav Choudhary, Choudhary, Tanav
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2507.18608

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/07/28

Abstract

The projective linear group PGL(3) naturally acts on the Grassmannian Gr(3, V₂) of 3-dimensional subspaces of the vector space V₂ of homogeneous conics in 3 variables. It was proved by Abdallah, Emsalem and Iarrobino in 2021 that this action has a one-parameter family of orbits along with 14 special orbits. The codimension 1 orbits of this action consist of the entire one-parameter family of orbits, along with 2 of the 14 special orbits. In this paper, we calculate the classes of the codimension 1 orbit closures in the Chow ring of Gr(3, V₂).

Citations

• The Hessian of elliptic curves as a Lattès map

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