Anthony Bak, Mount Holyoke College

Building Bundles with Specified Chern Classes on Abelian Surface Fibered Calabi-Yau's

Physical Considerations from Heterotic String Theory require the construction of vector bundle on Calabi-Yau threefolds with certain specified Chern Classes. We will review the requirements from physics and present the spectral construction for building bundles on Abelian Surface fibered Calabi-Yaus. The main technical tool will be the Fourier-Mukai transform. We will review it's basic properties discuss how to extend it from the classical case of a single abelian surface to a family of abelian surfaces (the main obstruction being how to handle the singular fibers). The talk will avoid discussion of technical details except where the illuminate some interesting problem.

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