  We compute the rational homology of the moduli stack $\mathcal{M}$ of objects
in the derived category of certain smooth complex projective varieties $X$
including toric varieties, flag varieties, curves, surfaces, and some 3- and
4-folds. We identify Joyce's vertex algebra construction on
$H_\ast(\mathcal{M},\mathbb{Q})$ with a generalized super-lattice vertex
algebra associated to $K^0_{\rm top}(X^{\rm an}) \oplus K^1_{\rm top}(X^{\rm
an})$.
