Geodesic
Quadrics of codimension two, and their automorphisms
Izvestiya. Mathematics , Tome 45 (1995) no. 1, pp. 151-174

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A study is made of nondegenerate quadrics of codimension two. An explicit description is given of their algebra of infinitesimal automorphisms. The dimension of this algebra is computed and estimated. The quadric with the richest automorphism group is determined. It is shown that in most cases all the automorphisms are linear. A holomorphic classification of quadrics is also given. 
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     author = {S. N. Shevchenko},
     title = {Quadrics of codimension two, and their automorphisms},
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S. N. Shevchenko. Quadrics of codimension two, and their automorphisms. Izvestiya. Mathematics , Tome 45 (1995) no. 1, pp. 151-174. http://geodesic.mathdoc.fr/item/IM2_1995_45_1_a6/