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Common Transversals and Tangents: The Ideal

After a suitable projective linear transformation

Using Plücker coordinates, the lines intersecting these 2 lines are given by

The quadric Q is given by the quadratic form associated to

and the condition of being tangent to it reformulates to

This leads to the formulation of the ideal as the 2-minors of the matrix

Here the c_ij stand for the coordinates of an 8-dimensional projective space. The Computational Aspect.

Sao Carlos, 08/02