The homology of moduli stacks of complexes

Jacob Gross

Published 2019-07-07Version 1

We compute the $E$-homology of the moduli stack $\mathcal{M}$ of objects in the derived category of a smooth complex projective variety $X$, where $E$ is a complex-oriented homology theory with rational coefficient ring. For curves, surfaces, and some 3- and 4-folds we identify Joyce's vertex algebra construction on $E_\ast(\mathcal{M})$ with a generalised super-lattice vertex algebra associated to $K^0_{\rm top}(X^{\rm an}) \oplus K^1_{\rm top}(X^{\rm an})$.