1. Invariants and projections of six lines in projective space
- Author
-
Dana Vazzana
- Subjects
Discrete mathematics ,Pure mathematics ,Applied Mathematics ,General Mathematics ,Complex projective space ,Projective line ,Projective space ,Projective plane ,Projective differential geometry ,Quaternionic projective space ,Pencil (mathematics) ,Mathematics ,Projective geometry - Abstract
Given six lines in P 3 \mathbf {P}^3 , quartics through the six lines define a map from P 3 \mathbf {P}^3 to P 4 \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.
- Published
- 2001