Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.
Relative Calabi-Yau structures II: Shifted Lagrangians in the moduli of objects
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abstract
We show that a Calabi-Yau structure of dimension $d$ on a smooth dg category $C$ induces a symplectic form of degree $2-d$ on the moduli space of objects $M_{C}$. We show moreover that a relative Calabi-Yau structure on a dg functor $C \to D$ compatible with the absolute Calabi-Yau structure on $C$ induces a Lagrangian structure on the corresponding map of moduli $M_{D} \to M_{C}$.
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Modules and generalizations of Joyce vertex algebras
Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.