Geodesic
Deformations of quadratic Diophantine systems
Izvestiya. Mathematics , Tome 65 (2001) no. 6, pp. 1085-1126

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We consider specializations of quadratic matrix equations preserving the invariant type of the equation and the weight formula for representations of the quadratic form by a genus of positive definite forms. We apply our results to the forms of cubic and Gosset lattices. 
@article{IM2_2001_65_6_a1,
     author = {V. G. Zhuravlev},
     title = {Deformations of quadratic {Diophantine} systems},
     journal = {Izvestiya. Mathematics },
     pages = {1085--1126},
     publisher = {mathdoc},
     volume = {65},
     number = {6},
     year = {2001},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2001_65_6_a1/}
}
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V. G. Zhuravlev. Deformations of quadratic Diophantine systems. Izvestiya. Mathematics , Tome 65 (2001) no. 6, pp. 1085-1126. http://geodesic.mathdoc.fr/item/IM2_2001_65_6_a1/