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.
Donaldson-Thomas theory for Calabi-Yau 4-folds
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Let $X$ be a compact complex Calabi-Yau 4-fold. Under certain assumptions, we define Donaldson-Thomas type deformation invariants ($DT_{4}$ invariants) by studying moduli spaces of solutions to the Donaldson-Thomas equations on $X$. We also study sheaves counting problems on local Calabi-Yau 4-folds. We relate $DT_{4}$ invariants of $K_{Y}$ to the Donaldson-Thomas invariants of the associated Fano 3-fold $Y$. When the Calabi-Yau 4-fold is toric, we adapt the virtual localization formula to define the corresponding equivariant $DT_{4}$ invariants. We also discuss the non-commutative version of $DT_{4}$ invariants for quivers with relations. Finally, we compute $DT_{4}$ invariants for certain Calabi-Yau 4-folds when moduli spaces are smooth and find a $DT_{4}/GW$ correspondence for $X$. Examples of wall-crossing phenomenon in $DT_{4}$ theory are also given.
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UNVERDICTED 4representative citing papers
Proves the Cao-Maulik-Toda conjecture equating GV invariants of fiber classes on a CY4 fibered over a curve with those of the smooth fiber under an orientation compatibility assumption.
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
Generalizes Joyce vertex algebras to non-linear enumerative problems and constructs twisted modules in the orthosymplectic case, proposing variants for different enumerative invariants.
citing papers explorer
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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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Gopakumar-Vafa invariants of fiber classes on Calabi-Yau 4-folds fibered over curves
Proves the Cao-Maulik-Toda conjecture equating GV invariants of fiber classes on a CY4 fibered over a curve with those of the smooth fiber under an orientation compatibility assumption.
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Defects, nested instantons and comet shaped quivers
Proposes comet-shaped quiver gauge theories for surface defects with nested instantons in 4D gauge theories on T^2 × T*C_{g,k} and gives conjectural explicit formulae for the virtual equivariant elliptic genus of bundles over nested Hilbert schemes of points on the affine plane.
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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.