Abstract
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 Poincaré sheaf. We find that in this case it induces an action of the modular group on the charges of 2-branes.
Highlights
It was used in [32, 33] to obtain the action that is induced by the Poincare sheaf on a basis of brane charges on a general elliptic Calabi-Yau X without reducible fibers
If we assume that our expressions for the S- and T -transformations still apply we find that for the two geometries studied in [26] the combination ZβQβ transforms exactly as it does for geometries with multiple sections
In this note we have explicitly calculated the action of a relative conifold transformation on a basis of central charges of B-branes for two classes of elliptically fibered CalabiYau varieties
Summary
It was used in [32, 33] to obtain the action that is induced by the Poincare sheaf on a basis of brane charges on a general elliptic Calabi-Yau X without reducible fibers. After discussing the examples we will calculate the action of the transformation on the 2-brane charges for arbitrary elliptically fibered Calabi-Yau varieties that can be constructed in the previously described manner.
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