Description
The command computes the Hodge numbers h^{p,q} of the smooth projective variety X. They are calculated as
HH^q(cotangentSheaf(p,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
