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Singularities of homogeneous quadratic mappings. (English) Zbl 1342.14116
The author considers the affine real variety \(V\) in \(\mathbb R^n\) defined as a zero level set of the mapping \(F\) into \(\mathbb{R}^2\), build of two quadratic forms. A complete topological description of \(V\) in all generic cases and the topology of the intersection of \(V\) with a half-space and the topology of various deformations of \(V_t\) are found. For the intersection of \(V\) and the half-space \(Z\), the author provides a complete description of its topological type in all but three isolated cases in dimension 4, and also in the diagonal case for generic \(V_t\).

MSC:
14P05 Real algebraic sets
58K05 Critical points of functions and mappings on manifolds
14J17 Singularities of surfaces or higher-dimensional varieties
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