Gopakumar-Vafa Invariants and Macdonald Formula
Abstract
In this paper, we present an investigation of the Gopakumar-Vafa (GV) invariant, a curve-counting integral invariant associated with Calabi-Yau threefolds, as proposed by physicists. Building upon the conjectural definition of the GV invariant in terms of perverse sheaves, as formulated by Maulik-Toda in 2016, we focus on the total space of the canonical bundle of and compute the relevant invariants. We establish a conjectural correspondence between the Gopakumar-Vafa and Pandharipande-Thomas invariants at the level of perverse sheaves, drawing inspiration from the work of Migliorini, Shende, and Viviani. This work serves as a significant step towards validating the conjecture and deepening our understanding of the GV invariant and its connections to algebraic geometry and physics.
Cite
@article{arxiv.2306.05547,
title = {Gopakumar-Vafa Invariants and Macdonald Formula},
author = {Lutian Zhao},
journal= {arXiv preprint arXiv:2306.05547},
year = {2023}
}