Degree two Gopakumar–Vafa invariants of local curves
Abstract
We investigate the Gopakumar-Vafa (GV) theory of local curves, namely, the total spaces of rank two vector bundles with canonical determinant on smooth projective curves. Under a certain genericity condition on the rank two bundles, we propose a general mechanism to compute the degree two GV invariants of local curves. In particular, we determine all the degree two GV invariants when the base curve has genus two. Combined with previous work by Bryan and Pandharipande, we obtain the GV/GW correspondence in this case. When the base curve has genus greater than two, we calculate GV invariants for some extremal genera, providing evidence for the GV/GW conjecture for curves of higher genus.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Numerical Analysis Techniques
Commutative Algebra and Its Applications
Publication details
- Journal / source
- Geometry & Topology
- Volume
- 30
- Issue
- 1
- Pages
- 307–336
- Publication date
- 19 January 2026
- Language
- EN