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arXiv · 2501.08633

Symmetrizer group of a projective hypersurface

Jun-Muk Hwang
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Abstract

To each projective hypersurface which is not a cone, we associate an abelian linear algebraic group called the symmetrizer group of the corresponding symmetric form. This group describes the set of homogeneous polynomials with the same Jacobian ideal and gives a conceptual explanation of results by Ueda--Yoshinaga and Wang. In particular, the diagonalizable part of the symmetrizer group detects Sebastiani-Thom property of the hypersurface and its unipotent part is related to the singularity of the hypersurface.

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Jun-Muk Hwang. 2025-01-15. Symmetrizer group of a projective hypersurface. https://arxiv.org/abs/2501.08633

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