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

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.

arXiv commentThe proof of the consistence contains a mistake that cannot be fixed

References in corpus (6)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Donaldson-Thomas invariants via microlocal geometry
• Symmetries and stabilization for sheaves of vanishing cycles
• Geometric Transitions
• Shifted Symplectic Structures
• Invariance of orientation data for ind-constructible Calabi-Yau $A_{\infty }$ categories under derived equivalence

Cited by in corpus (4)

• Orientability for gauge theories on Calabi-Yau manifolds
• Categorification of Donaldson-Thomas invariants via Perverse Sheaves
• Perversely categorified Lagrangian correspondences
• On motivic Joyce-Song formula for the Behrend function identities