The homology of moduli stacks of complexes

Abstract

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 $K_{\mathrm{top}}^0(X^{\mathrm{an}})\oplus K_{\mathrm{top}}^1(X^{\mathrm{an}})$.

de-emphasized complex-oriented theories