The intersection conics of six straight lines. (English) Zbl 1090.51008

Schröcker, Hans-Peter

Beitr. Algebra Geom. 46, No. 2, 435-446 (2005).

The paper refers to the manifold \(M\) of planes that intersect six straight lines of the real projective three-dimensional space in points of a conic. After characterizing the line configurations that yield a manifold of dimension three, the author shows that in general \(M\) is algebraic of dimension two and class eight. The lines on \(M\) are characterized under the hypothesis that no three basic lines are coplanar or concurrent. Algorithms for computation of the equation of \(M\) and of solution planes are devised. The proofs are based on Pascal’s theorem and a previous result of the author [J. Geom. 73, 134–147 (2002; Zbl 1006.51016)].

Reviewer: Mihai Cipu (Bucureşti)

MSC:

51N15	Projective analytic geometry
51N35	Questions of classical algebraic geometry
14N10	Enumerative problems (combinatorial problems) in algebraic geometry

Keywords:

incidence; conic section; Pascal’s theorem

Citations:

Zbl 1006.51016