Symmetrizer group of a projective hypersurface
Algebraic Geometry
2025-01-16 v1
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.
Keywords
Cite
@article{arxiv.2501.08633,
title = {Symmetrizer group of a projective hypersurface},
author = {Jun-Muk Hwang},
journal= {arXiv preprint arXiv:2501.08633},
year = {2025}
}
Comments
to appear in J. Math. Soc. Japan