Gopakumar-Vafa invariants and wall-crossing

Abstract

In this paper, we generalize a mathematical definition of Gopakumar-Vafa (GV) invariants on Calabi-Yau 3-folds introduced by Maulik and the author, using an analogue of BPS sheaves introduced by Davison-Meinhardt on the coarse moduli spaces of one dimensional twisted semistable sheaves with arbitrary holomorphic Euler characteristics. We show that our generalized GV invariants are independent of twisted stability conditions, and conjecture that they are also independent of holomorphic Euler characteristics, so that they define the same GV invariants. As an application, we will show the flop transformation formula of GV invariants.

53 pages, Appendix A is removed and the proof of Prop 5.3 is modified

References in corpus (3)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Moduli stacks of semistable sheaves and representations of Ext-quivers
• Generalized Donaldson-Thomas theory over fields K $\ne$ C

Cited by in corpus (7)

• Moduli stacks of semistable sheaves and representations of Ext-quivers
• Birational geometry for d-critical loci and wall-crossing in Calabi-Yau 3-folds
• BPS Lie algebras and the less perverse filtration on the preprojective CoHA
• The local motivic DT/PT correspondence
• Refined invariants of finite-dimensional Jacobi algebras
• Orientation data for coherent sheaves on the local projective plane
• On the intersection cohomology of the moduli of ${\mathrm{SL}}_n$-Higgs bundles on a curve