Conical, ruled and deficiency one translation planes

Flocks of deficiency one of quadratic cones and hyperbolic quadrics in PG(3 , K), for K a finite field, correspond to translation planes admitting cert ain collineation groups that fix Baer subplanes pointwise. In this article, this theory is extended to the general situation where K is an arbitrary f ield. Flocks of quadratic cones and of hyperbolic quadrics in PG(3, q) corr espond to spreads in PG(3, q) which are unions of q or q + 1 reguli respect ively. A more general theory of the analogous conical and ruled spreads is developed for spreads in PG(3, K) and K an arbitary skewfield.