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This is a Quantitative Study study.

October 10, 2025Open Access

Several sufficient conditions for projective hypersurfaces to be GIT (semi)stable

Key Points

Sufficient conditions for GIT semi-stability depend on dimension and degree of hypersurfaces.
Isolated singularities with multiplicity 2 allow analysis of stability through Hessian matrix ranks.
Dimension of the singular locus plays a critical role in determining stability conditions.
The study provides a framework for assessing projective hypersurfaces in algebraic geometry.

Abstract

In this paper, I present some sufficient conditions for projective hypersurfaces to be GIT (semi-)stable. These conditions will be presented in terms of dimension and degree of the hypersurfaces, dimension of the singular locus and multiplicities of the singular points. When singularities of the hypersurface are isolated and all have multiplicity 2, we can judge its stability via the ranks of Hessian matrices at these singular points.

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Cite This Study

X. He (Sat,) studied this question.

synapsesocial.com/papers/68e865117ef2f04ca37e4dbb https://doi.org/https://doi.org/10.48550/arxiv.2510.03695

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