Invariants and projections of six lines in projective space

Vazzana, Dana

doi:10.1090/S0002-9947-01-02742-8

Invariants and projections of six lines in projective space
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by Dana R. Vazzana

Trans. Amer. Math. Soc. 353 (2001), 2673-2688

DOI: https://doi.org/10.1090/S0002-9947-01-02742-8

Published electronically: January 18, 2001

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Abstract:

Given six lines in $\mathbf {P}^3$, quartics through the six lines define a map from $\mathbf {P}^3$ to $\mathbf {P}^4$, and the image of this map is described in terms of invariants of the six lines. The map can be interpreted as projection of the six lines, and this permits a description of the canonical model of the octic surface which is given by points which project the lines so that they are tangent to a conic. We also define polarity for sets of six lines, and discuss the above map in the case of a self-polar set of lines and in the case of six lines which form a “double-sixer” on a cubic surface.

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