hh^(p,q)(X)
As an example we compute h^11 of a K3 surface (Fermat quartic in projective threespace:
i1 : X = Proj(QQ[x_0..x_3]/ideal(x_0^4+x_1^4+x_2^4+x_3^4)) o1 = X o1 : ProjectiveVariety
i2 : hh^(1,1)(X) o2 = 20
The object hh is a scripted functor.