Genus zero Gopakumar-Vafa invariants of Multi-Banana configurations

Abstract

The multi-Banana configuration ${\hat{F}}_{mb}$ is a local Calabi-Yau threefold of Schoen type. Namely, ${\hat{F}}_{mb}$ is a conifold resolution of ${\hat{I}}_v{\times }_{\mathbf{D}}{\hat{I}}_w$, where ${\hat{I}}_v\to \mathbf{D}$ is an elliptic surface over a formal disc $\mathbf{D}$ with an $I_v$ singulararity on the central fiber. We generalize the technique developed in our earlier paper to compute genus 0 Gopakumar-Vafa invariants of certain fiber curve classes. We illustrate the computation explicitly for $v=1$ and $v=w=2$. The resulting partition function can be expressed in terms of elliptic genera of ${\mathbf{C}}^2$, or classical theta functions, respectively.

References in corpus (1)

• The Donaldson-Thomas partition function of the banana manifold