A Dimension Bound for Symmetrizer Groups of Projective Hypersurfaces
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910104545132544 |
|---|---|
| author | Jung, Jegyeong |
| author_facet | Jung, Jegyeong |
| contents | Let $X$ be a projective hypersurface that is not a cone. The symmetrizer group of $X$ is an algebraic group parametrizing hypersurfaces whose Jacobian ideal coincides with that of $X$. We show that if the locus of points in $X$ with multiplicity $d-1$ does not contain a line, then the dimension of the nilpotent part of the Lie algebra associated to the symmetrizer group is at most $2$, and the dimension of the symmetrizer group is bounded by $\dim X + 2$. To achieve this, we investigate the relation between a class of singularities on $X$ with highly degenerate tangent cones and the unipotent part of its symmetrizer group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_19642 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Dimension Bound for Symmetrizer Groups of Projective Hypersurfaces Jung, Jegyeong Algebraic Geometry 14J70, 14J17 Let $X$ be a projective hypersurface that is not a cone. The symmetrizer group of $X$ is an algebraic group parametrizing hypersurfaces whose Jacobian ideal coincides with that of $X$. We show that if the locus of points in $X$ with multiplicity $d-1$ does not contain a line, then the dimension of the nilpotent part of the Lie algebra associated to the symmetrizer group is at most $2$, and the dimension of the symmetrizer group is bounded by $\dim X + 2$. To achieve this, we investigate the relation between a class of singularities on $X$ with highly degenerate tangent cones and the unipotent part of its symmetrizer group. |
| title | A Dimension Bound for Symmetrizer Groups of Projective Hypersurfaces |
| topic | Algebraic Geometry 14J70, 14J17 |
| url | https://arxiv.org/abs/2603.19642 |