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arXiv · 2212.09364

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

Masafumi Hattori·Aline Zanardini
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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.

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Masafumi Hattori, Aline Zanardini. 2022-12-19. On the GIT stability of linear systems of hypersurfaces in projective space. https://doi.org/10.4171/rmi%2F1544

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