The quantum loop algebra $U_{v}(\mathcal{L}\mathfrak{g})$ was defined as a
generalization of the Drinfeld's new realization of quantum affine algebra to
the loop algebra of any Kac-Moody algebra $\mathfrak{g}$. Schiffmann \cite{S}
has proved (and conjectured) that the Hall algebra of the category of coherent
sheaves over weighted projective lines provides a realization of
$U_{v}(\mathcal{L}\mathfrak{g})$ for those $\mathfrak{g}$ associated to a
star-shaped Dynkin diagram.