Invariants and projections of lines in projective space.

An overview of geometric invariant theory as it applies to moduli spaces of point and line configurations is given. Given five lines in P$\sp3$ and a fixed plane, a map from P$\sp3$ to the moduli space of sets of five lines in the projective plane is given via projection and its fibres are described. Given six lines in P$\sp3,$ quartics through the six lines define a map from P$\sp3$ to P$\sp4,$ 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.PhDMathematicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/131562/2/9910014.pd