For non-cone projective hypersurfaces where the (d-1)-multiplicity locus contains no line, the symmetrizer group dimension is bounded by dim X + 2 and its nilpotent Lie algebra part by 2.
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A Dimension Bound for Symmetrizer Groups of Projective Hypersurfaces
For non-cone projective hypersurfaces where the (d-1)-multiplicity locus contains no line, the symmetrizer group dimension is bounded by dim X + 2 and its nilpotent Lie algebra part by 2.