Definitions: Flock, Star Flock,Monomial Flock, Dual Setting, Semi-Field Type Flock

Proposition 11.2.5: Let F = F(ta, t, tb) be a monomial semi-field type flock in PG(3,q) with q = pn for some prime p, a = pi, b = pj with 0 < i < j < n. Let d = gcd(i,j,n), and n' = n/d. The configuration of points in W' = 0 which are the intersections of the lines of DF with W' = 0 is an embedded PG(n'-1,pd). Furthermore, if n 3d, then this configuration is not contained in a line. Also, the points of W' = 0 off of the three lines X' = 0, Y' = 0 and Z' = 0 can be partitioned into disjoint copies of the embedded PG(n'-1,pd).

Pf: Coming soon.

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