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The homology of moduli stacks of complexes

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arxiv 1907.03269 v3 pith:QRKMNCOE submitted 2019-07-07 math.AG

The homology of moduli stacks of complexes

classification math.AG
keywords varietiesalgebrahomologymathcalmodulivertexassociatedcategory
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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 $K^0_{\rm top}(X^{\rm an}) \oplus K^1_{\rm top}(X^{\rm an})$.

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Cited by 5 Pith papers

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