Communications in Analysis and Geometry
Volume 21 (2013)
Donaldson–Thomas invariants of certain Calabi–Yau 3-folds
Pages: 541 – 578
We compute the Donaldson–Thomas invariants for two types of Calabi–Yau 3-folds. These invariants are associated to the moduli spaces of rank-2 Gieseker semistable sheaves. None of the sheaves are locally free, and their double duals are locally free stable sheaves investigated earlier in [12, 25, 33]. We show that these Gieseker moduli spaces are isomorphic to some Quot-schemes. We prove a formula for Behrend’s $ν$-functions when torus actions present with positive dimensional fixed point sets, and use it to obtain the generating series of the relevant Donaldson–Thomas invariants in terms of the McMahon function.