Categorification of Donaldson-Thomas invariants by Perverse Sheaves

TL;DR

This paper constructs a perverse sheaf on the moduli space of semistable sheaves on a Calabi-Yau 3-fold, linking it to Donaldson-Thomas invariants via a new cohomology theory.

Contribution

It introduces a natural perverse sheaf on the moduli space that captures Donaldson-Thomas invariants through vanishing cycles and local Chern-Simons functionals.

Findings

Perverse sheaf constructed on the moduli space.

Cohomology theory whose Euler numbers equal DT invariants.

Connection between sheaf theory and enumerative geometry.

Abstract

We show that there is a natural perverse sheaf on the moduli space of semistable sheaves on a smooth projective Calabi-Yau 3-fold which is locally the perverse sheaf of vanishing cycles for a local Chern-Simons functional. This gives us a cohomology theory whose Euler numbers are Donaldson-Thomas invariants.