A theory of generalized Donaldson–Thomas invariants

Donaldson–Thomas invariants D T α ( τ ) DT^α (τ ) are integers which ‘count’ τ τ -stable coherent sheaves with Chern character α α on a Calabi–Yau 3-fold X X , where τ τ denotes Gieseker stability for some ample line bundle on X X . They are unchanged under deformations of X X . The conventional definition works only for classes α α containing no strictly τ τ -semistable sheaves. Behrend showed that D T α ( τ ) DT^α (τ ) can be written as a weighted Euler characteristic χ ( M s t α ( τ ) , ν M <mml:mi mathvariant="