${\rm U}(n)$ vector bundles on Calabi-Yau three-folds for string theory compactifications

An explicit description of the spectral data of stable U (n) vector bundles on elliptically fibered Calabi–Yau three-folds is given, extending previous work of Friedman, Morgan and Witten. The characteristic classes are computed and it is shown that part of the bundle cohomology vanishes. The stability and the dimension of the moduli space of the U (n) bundles are discussed. As an application, it is shown that the U (n)

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