On the GIT stability of linear systems of hypersurfaces in projective space

2022/12/19 by Masafumi Hattori, Hattori, Masafumi, Aline Zanardini +1
Materials Science · Mathematics · #14E99 (Secondary) #14L24 (Primary) 14J27 #Advanced Differential Equations and Dynamical Systems #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #Synthesis and properties of polymers

paper · pdf · doi:10.48550/arxiv.2212.09364

openalex publication_date 2022/12/19 · openalex created_date 2023/01/04 · openalex updated_date 2026/07/28

Abstract

We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem completely. As an application, we consider a few relevant geometric examples recovering, for instance, Miranda's description of the GIT stability of pencils of plane cubics. Furthermore, we completely describe the GIT stability of Halphen pencils of any index.

Related

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• GIT stability of linear maps on projective space with marked points
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• GIT stability of divisors in products of projective spaces