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Abstract

This research develops a method to compute Katz's genus 0 Gopakumar-Vafa invariants of fiber curve classes of the Banana manifold, a smooth compact Calabi-Yau threefold, and its generalizations, the multi-Banana configurations. The invariants turn out to have geometric significance, being an actual count of certain local configurations of rational curves on a related threefold. In both these cases, the partition functions for the invariants exhibit a modularity and can be expressed in terms of Jacobi forms or theta functions.