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The homology of moduli stacks of complexes
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The homology of moduli stacks of complexes
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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 $K^0_{\rm top}(X^{\rm an}) \oplus K^1_{\rm top}(X^{\rm an})$.
Forward citations
Cited by 5 Pith papers
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Rationality and symmetry of stable pairs generating series of Fano 3-folds
Generating series of stable pairs descendent invariants on Fano 3-folds are rational and q ↔ q^{-1} symmetric.
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Wall-crossing for Calabi-Yau fourfolds: framework, tools, and applications
Establishes wall-crossing for Calabi-Yau four dg-quivers and local CY fourfolds via refined vertex algebras and a new stable infinity-categorical framework for virtual pullbacks.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
Proves that generating functions of Pandharipande-Thomas invariants with descendent insertions are rational with controlled poles for superpositive curve classes on projective complex 3-manifolds.
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The Pandharipande-Thomas rationality conjecture for superpositive curve classes on projective complex 3-manifolds
PT generating functions with descendents are rational, with controlled poles, for superpositive curve classes on projective complex 3-folds.
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Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing
Explicit PT descendent large-n tails on P3, cubic threefolds and blow-ups are obtained by one-dimensional wall-crossing and agree with known formulas up to Laurent polynomials.
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