On GIT stability of linear systems of hypersurfaces in projective spaces

• Masafumi Hattori ^[1] ; Aline Zanardini ^[2]
  1. [1] Kyoto University

     Kyoto University

     Kamigyō-ku, Japón

     
  2. [2] École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 41, Nº 3, 2025, págs. 807-836
• Idioma: inglés
• DOI: 10.4171/RMI/1544
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• Resumen

  • In this paper, we consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in projective space up to projective equivalence. Our main result consists of a complete criterion for (semi)stability in the sense of geometric invariant theory (GIT). As an application, we inspect a few relevant geometric examples recovering, for instance, Miranda’s characterization of GIT stability of pencils of plane cubics. Furthermore, we completely describe GIT stability of Halphen pencils of any index.