The Veronese Surface in PG
نویسنده
چکیده
A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, 6, 1) design, the blocks being the hyperplane sections containing more than three (actually six) points of K. As such a point model is projectively unique, the present construction yields an easy coordinate–free approach to some results obtained independently by H.S.M. Coxeter and G. Pellegrino, including a projective representation of the Mathieu group M12 in PG(5, 3). ∗Research supported by the Austrian FWF, project P12353–MAT.
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Applications of line geometry, III: The quadric Veronesean and the chords of a twisted cubic
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