# hh -- Hodge numbers of a smooth projective variety

## Synopsis

• Usage:
hh^(p,q)(X)
• Inputs:
• a pair (p,q) of non negative integers
• Outputs:

## 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

## Caveat

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