Orientation data on moduli space of sheaves on Calabi-Yau threefold

2012/12/16 by Hua, Zheng
#Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1212.3790

Abstract

Kontsevich and Soibelman introduced a notion of orientation data on Calabi-Yau category. It can be viewed as a consistent choice of spin structure on moduli space of objects in the given category. The orientation data plays an important role in Donaldson-Thomas theory. Let X be a projective, simply connected and torsion free CY 3-fold. We prove the existence of orientation data for the moduli space of coherent sheaves on X.

Related

• Orientation data for moduli spaces of coherent sheaves over Calabi-Yau 3-folds
• Invariance of orientation data for ind-constructible Calabi-Yau\n A_\∞ categories under derived equivalence
• Orientations for DT invariants on quasi-projective Calabi-Yau 4-folds
• Orientation data for coherent sheaves on the local projective plane
• Bordism categories and orientations of moduli spaces