2013/09/17 by Cao, Yalong
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1309.4230
Let X be a complex four-dimensional compact Calabi-Yau manifold equipped with a Kähler form ω and a holomorphic four-form Ω. Under certain assumptions, we define Donaldson-Thomas type deformation invariants by studying the moduli space of the solutions of Donaldson-Thomas equations on the given Calabi-Yau manifold. We also study sheaves counting on local Calabi-Yau four-folds. We relate the sheaves countings over KY with the Donaldson-Thomas invariants for the associated compact three-fold Y. In some very special cases, we prove the DT/GW correspondence for X. Finally, we compute the Donaldson-Thomas invariants of certain Calabi-Yau four-folds when the moduli spaces are smooth.