Genus zero Gopakumar-Vafa invariants of Multi-Banana configurations

2021/02/16 by Morishige, Nina
#11F50 #14D20 (Secondary) #14D21 #14J30 #14J32 #14N35 (Primary) #32Q25 #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2102.07965

Abstract

The multi-Banana configuration \widehatF_mb is a local Calabi-Yau threefold of Schoen type. Namely, \widehatF_mb is a conifold resolution of \widehatI_v ×_\bfD \widehatI_w, where \widehatI_v → \bfD is an elliptic surface over a formal disc \bfD 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 \bfC², or classical theta functions, respectively.

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