Categorification of Donaldson-Thomas invariants via Perverse Sheaves

Young-Hoon Kiem, Jun Li

Published 2012-12-23, updated 2016-03-21Version 5

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.