The multi-Banana configuration $\widehat{ F}_{ mb}$ is a local Calabi-Yau threefold of Schoen type. Namely, $\widehat{ F}_{ mb}$ is a conifold resolution of $\widehat{ I}_v \times_{ \bf{ D}} \widehat{ I}_w$, where $\widehat{ I}_v \to { \bf{ D}}$ is an elliptic surface over a formal disc ${ \bf{ D}}$ 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 $\bf{ C}^2$, or classical theta functions, respectively.
Categories: math.AG hep-th