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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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/

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