  We give a combinatorial model for the bounded derived category of graded
modules over the dual numbers in terms of arcs on the integer line with a point
at infinity. Using this model we describe the lattice of thick subcategories of
the bounded derived category, and of the perfect complexes, in terms of
non-crossing partitions. We also make some comments on the symmetries of these
lattices, exceptional collections, and the analogous problem for the unbounded
derived category.
