Mukai lifting of self-dual points in ℙ⁶

2024/06/04 by B. Betti, Leonie Kayser, Betti, Barbara +1 · 2 citations
Mathematics · #13H10 #14D22 #14N05 #65H14 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2406.02734

openalex publication_date 2024/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A set of 2n points in ℙ^n-1 is self-dual if it is invariant under the Gale transform. Motivated by Mukai's work on canonical curves, Petrakiev showed that a general self-dual set of 14 points in ℙ⁶ arises as the intersection of the Grassmannian \rm Gr(2,6) in its Plücker embedding in ℙ¹⁴ with a linear space of dimension 6. In this paper we focus on the inverse problem of recovering such a linear space associated to a general self-dual set of points. We use numerical homotopy continuation to approach the problem and implement an algorithm in Julia to solve it. Along the way we also implement the forward problem of slicing Grassmannians and use it to experimentally study the real solutions to this problem.

Cited by

• A combinatorial description of when a self-associated set of points fails to be arithmetically Gorenstein
• The SagbiHomotopy.jl package for solving polynomial systems

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