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We extend the Spectral Construction, a technique used with great success tostudy and construct vector bundles on elliptically fibered varieties, to aspecial family of abelian surface fibered varieties. The results are motivatedby requirements from Heterotic String Phenomenology where vector bundles withspecified chern class are required to produce a realistic particle spectrum.Although only certain (1,8)-polarized families of abelian surfaces areconsidered here we expect the main ideas to carry over to other families ofabelian varieties with a uniform relative polarization type.

The Spectral Construction for a (1,8)-Polarized Family of Abelian Varieties