Geodesic
Quadrics of codimension 4 in $\mathbb C^7$ and their automorphisms
Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 803-811

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Automorphisms of nondegenerate $(4,3)$-quadrics are studied. We classify quadrics of this kind with nonlinear automorphisms and find the dimensions of their groups of automorphisms. 
@article{MZM_1998_64_6_a0,
     author = {E. G. Anisova},
     title = {Quadrics of codimension 4 in $\mathbb C^7$ and their automorphisms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--811},
     publisher = {mathdoc},
     volume = {64},
     number = {6},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a0/}
}
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E. G. Anisova. Quadrics of codimension 4 in $\mathbb C^7$ and their automorphisms. Matematičeskie zametki, Tome 64 (1998) no. 6, pp. 803-811. http://geodesic.mathdoc.fr/item/MZM_1998_64_6_a0/