Topological string partition function on CY threefolds factors into conifold terms powered by sheaf invariants, enabling non-perturbative Borel-resummed expression whose jumps are controlled by genus-zero GV invariants and a deformed prepotential.
Categorification of Donaldson-Thomas invariants via Perverse Sheaves
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abstract
We show that there is a perverse sheaf on a fine moduli space of stable sheaves on a smooth projective Calabi-Yau 3-fold, which is locally the perverse sheaf of vanishing cycles for a local Chern-Simons functional, possibly after taking an etale Galois cover. This perverse sheaf lifts to a mixed Hodge module and gives us a cohomology theory which enables us to define the Gopakumar-Vafa invariants mathematically.
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Shifted symplectic structures are built on rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension two or higher, with a proof that B G_m actions are Hamiltonian and a new rigidification functor as left adjoint.
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Non-perturbative topological strings from resurgence
Topological string partition function on CY threefolds factors into conifold terms powered by sheaf invariants, enabling non-perturbative Borel-resummed expression whose jumps are controlled by genus-zero GV invariants and a deformed prepotential.
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Shifted symplectic rigidification
Shifted symplectic structures are built on rigidified moduli spaces of sheaves on Calabi-Yau varieties of dimension two or higher, with a proof that B G_m actions are Hamiltonian and a new rigidification functor as left adjoint.