Geodesic
Resolutions of Singularities of Varieties of Lie Algebras of Dimensions 3 and 4
Journal of Lie theory, Tome 12 (2002) no. 2, pp. 397-407
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We determine the singular points and a resolution of singularities of each irreducible component of the varieties of the Lie algebras of dimension 3 and 4 over C. 
@article{JLT_2002_12_2_JLT_2002_12_2_a4,
     author = {R. Basili},
     title = {Resolutions of {Singularities} of {Varieties} of {Lie} {Algebras} of {Dimensions} 3 and 4},
     journal = {Journal of Lie theory},
     pages = {397--407},
     year = {2002},
     volume = {12},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a4/}
}
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R. Basili. Resolutions of Singularities of Varieties of Lie Algebras of Dimensions 3 and 4. Journal of Lie theory, Tome 12 (2002) no. 2, pp. 397-407. http://geodesic.mathdoc.fr/item/JLT_2002_12_2_JLT_2002_12_2_a4/