Macaulay2Doc :: hh

- Usage:
`hh^(p,q)(X)`

- Inputs:
- a pair
`(p,q)`of non negative integers `X`, a projective variety

- a pair
- Outputs:
- an integer

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 |

There is no check made if the projective variety X is smooth or not.

- HH^ZZ SumOfTwists -- coherent sheaf cohomology module
- HH^ZZ SheafOfRings -- cohomology of a sheaf of rings on a projective variety
- euler(ProjectiveVariety) -- topological Euler characteristic of a (smooth) projective variety

- hh(Sequence,ProjectiveVariety)
`hh^ZZ(Sequence)`(missing documentation)

The object hh is a scripted functor.