In the previous paper [N3], we introduced a cofree embedding of a finite dimensional rational representation of a diagonalizable algebraic group over an algebraically closed field of characteristic zero. Using this, we show inductive characterization of toric locally complete intersection singularities in terms of group representation theory. Consequently we obtain a classification of affine monomial normal hypersurfaces.
Haruhisa Nakajima. "Invariant theoretical characterization of toric locally complete intersection singularities." Proc. Japan Acad. Ser. A Math. Sci. 82 (9) 161 - 166, December 2006. https://doi.org/10.3792/pjaa.82.161