Investigation of a real algebraic surface

A description of a real algebraic variety in ℝ3 is given. This variety plays an important role in the investigation of the Einstein metrics whose evolution is studied using the normalized Ricci flow. To reveal the internal structure of this variety, a description of all its singular points is given. Due to the internal symmetry of this variety, a part of the investigation uses elementary symmetric polynomials. All the computations are performed using computer algebra algorithms (in particular, Gröbner bases) and algorithms for dealing with polynomial ideals. As an auxiliary result, a proposition about the structure of the discriminant surface of a cubic polynomial is proved.

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