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Instability and Singularity of Projective Hypersurfaces

Abstract

In this paper, we will show that the Hesselink stratification of a Hilbert scheme of hypersurfaces is independent of the choice of Pl\"ucker coordinate and there is a positive relation between the length of Hesselink's worst virtual 1-parameter subgroup and multiplicity of a projective hypersurface.Comment: -Corrected the fractional power of determinants in the proof of Theorem 3.1 -Corrected explanations of lemmas and the theorem in the last sectio

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