Hodge structure
= Hodge structure
{c}
{title2=$H_{\mathbb C}=\bigoplus_{p+q=w}H^{p,q}$}
{wiki}
A pure integral Hodge structure is a finite-rank free abelian group with a complex decomposition satisfying $\overline{H^{p,q}}=H^{q,p}$ and $p+q=w$. The integer $w$ is its weight. Its equivalent <Hodge filtration> is $F^p=\bigoplus_{r\ge p}H^{r,w-r}$.