On GIT stability of linear systems of hypersurfaces in projective spaces

Hattori, MasafumiZanardini, Aline2025-05-052025-05-052025-05-02202510.4171/RMI/15442-s2.0-105003438523https://infoscience.epfl.ch/handle/20.500.14299/249704In 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.truegeometric invariant theoryHalphen pencilslinear systems of hypersurfacesOn GIT stability of linear systems of hypersurfaces in projective spacestext::journal::journal article::research article