The Gopakumar-Vafa finiteness conjecture
arXiv:2103.08221
Abstract
The Gopakumar-Vafa conjecture predicts that the BPS invariants of a symplectic 6-manifold, defined in terms of the Gromov-Witten invariants, are integers and all but finitely many vanish in every homology class. The integrality part of this conjecture was proved earlier by Ionel and Parker. This article proves the finiteness part. The proof relies on a modification of Ionel and Parker's cluster formalism using results from geometric measure theory.
v2: accepted for publication in Annals of Mathematics
References in corpus (6)
- Curve counting via stable pairs in the derived category
- Stable pairs and BPS invariants
- Relative Lefschetz Action and BPS State Counting
- Categorification of Donaldson-Thomas invariants via Perverse Sheaves
- Castelnuovo's bound and rigidity in almost complex geometry
- Counting embedded curves in symplectic 6-manifolds