The homology of moduli stacks of complexes

2019/07/07 by Jacob Gross, Gross, Jacob · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1907.03269

Abstract

We compute the rational homology of the moduli stack 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_∗(M,ℚ) with a generalized super-lattice vertex algebra associated to K⁰_{\rm top}(X^{\rm an}) ⊕ K¹_{\rm top}(X^{\rm an}).

Citations

• Donaldson-Thomas theory for Calabi-Yau 4-folds
• Lectures on K-theoretic computations in enumerative geometry

Cited by

• Enumerative invariants and wall-crossing formulae in abelian categories
• Modules and generalizations of Joyce vertex algebras

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