Geodesic
Quadratic forms and quadrics of space over local rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 3, pp. 97-110

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Relatively recent and new results on the enumeration of classes of projective congruent quadrics and classes of projective equivalent quadrics of projective spaces over a local ring $R=2R$ with nilpotent principal maximal ideal are reflected in the paper. For the case of the basic ring $R$ with nonprincipal maximal ideal, the enumerations of quadrics of projective plane are given up to projective equivalence. 
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     author = {O. A. Starikova},
     title = {Quadratic forms and quadrics of space over local rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {97--110},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2012_17_3_a7/}
}
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O. A. Starikova. Quadratic forms and quadrics of space over local rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 17 (2012) no. 3, pp. 97-110. http://geodesic.mathdoc.fr/item/FPM_2012_17_3_a7/