Categorification of Donaldson-Thomas invariants via Perverse Sheaves

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.

Completely rewritten. 94 pages

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Symmetries and stabilization for sheaves of vanishing cycles
• Orientation data on moduli space of sheaves on Calabi-Yau threefold

Cited by in corpus (16)

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• Counting embedded curves in symplectic 6-manifolds
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• Crystal Melting, BPS Quivers and Plethystics
• Gopakumar-Vafa invariants via vanishing cycles
• On motivic Joyce-Song formula for the Behrend function identities
• Derived stacks in symplectic geometry
• The Gopakumar-Vafa finiteness conjecture
• Topological strings, quiver varieties and Rogers-Ramanujan identities
• Batalin--Vilkovisky quantization and supersymmetric twists
• The moduli space of stable coherent sheaves via non-archimedean geometry
• Intersection theories of coherent sheaf stacks and virtual pull-backs via semi-perfect obstruction theories
• Note on the motivic DT/PT correspondence and the motivic Flop formula