The intersection rings of the conic varieties (Q1177858)

We intend to compute the intersection rings of the conic varieties \(N(\overline M)\) which we defined in Beitr. Algebra Geom. 30, 117-133 (1990; Zbl 0758.14020). These varieties may be understood as all of the possible finite sequences of blowing-ups of the classical variety of complete conics along the \(G\)-stable 3-subvarieties. The group action on \(N(\overline M)\) is defined by the action of \(G=GL(3)\) on the projective plane in which the point conics lie. We shall describe the intersection rings over \(\mathbb{Q}\) in terms of factor rings of polynomial rings.