  I show that the weighted projective line PP(2,3) has an embedding PP(2,3)
into PP(4,5,6,9) whose image Gamma is contained in a quasismooth K3
hypersurface X_24 in PP(4,5,6,9). The pair (Gamma in X_24) unprojects to the
codimension 4 K3 surface Y in PP(4,5,5,6,7,8,9) with
  Basket = [1/2(1,1), 1/5(1,4), 1/5(2,3), 1/9(4,5)],
  Hilbert Numerator = 1 - t^12 - t^13 - 2t^14 - 2t^15 - 2t^16 - t^17
  + t^19 + 2t^20 + 3t^21 + 4t^2 + 3t^23 + ..
  (this example is called Altinok4(111) in the Magma K3 database). The local
coordinates at the third centre P_3 = 1/5(2,3) of Y are of weight 7 and 8
(rather than 2 and 3), so both are eliminated by the projection from P_3.
Together with other examples, this gives substance to Type IV unprojections.
Several more cases of Type IV unprojections are known up to codimension 5 or 6.
The paper also contains some Magma programming routines suitable as exercises
for babies.
