Resolvable designs are block designs with the additional property that the blocks can be partitioned into partitions of the points. It is easy to see that lines in affine space form a resolvable design since parallel lines partition the space, and so we can partition the lines according to direction.


Can lines in projective space form a resolvable design? 


(Unlike affine spaces, this will not be the case for all projective spaces.)



Resolvable designs from projective space
The fact that every odd dimensional projective geometry ${\rm PG}(n,2)$ over $\mathbb{F}\_2$ admits a line parallelism (i.e., the Steiner $2$-design formed by the points and lines of ${\rm PG}(n,2)$ with $n$ odd is resolvable) is a corollary of the classical result proven here:


[R. D. Baker, *Partitioning the planes of* ${\rm AG}\_{2m}(2)$ *into* $2$-*designs*, Discrete Math. **15** (1976), 205–211](http://www.sciencedirect.com/science/article/pii/0012365X7690025X)


Edit: Note that Nick's comment about this result is apparently assuming the trivial necessary condition: the corresponding Steiner $2$-design for when $n$ is even can't be resolvable because in this case the number of points is not divisible by the block size.


For ${\rm PG}(n,q)$ with $q \not= 2$, all I know is Beutelspacher's result Nick mentioned (i.e., the case when $n = 2^{i+1}-1$).


If there are newer positive results, I'm not aware of them. In any case, here's a survey of parallelisms of projective spaces written in 2003:


[N. L. Johnson, *Parallelisms of projective spaces*, J. Geometry, **76** (2003), 110-182](http://link.springer.com/article/10.1007/s00022-003-1695-x)


