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Modularity from Monodromy

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arxiv 1902.08215 v1 pith:KZTZ2VNE submitted 2019-02-21 hep-th math.AG

Thorsten Schimannek This is my paper · ORCID
classification hep-thmath.AG
keywords actionchargesfourier-mukaisectionsheafadmitbasisbrane
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In this note we describe a method to calculate the action of a particular Fourier-Mukai transformation on a basis of brane charges on elliptically fibered Calabi-Yau threefolds with and without a section. The Fourier-Mukai kernel is the ideal sheaf of the relative diagonal and for fibrations that admit a section this is essentially the Poincar\'e sheaf. We find that in this case it induces an action of the modular group on the charges of 2-branes.

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  1. Revisiting the Quantum Geometry of Torus-fibered Calabi-Yau Threefolds

    hep-th 2025-10 conditional novelty 7.0 of 10

    The conjectured Jacobi modularity of topological string amplitudes on torus-fibered Calabi-Yau threefolds is derived conditionally from the wave-function property under the relative conifold monodromy, which also maps...

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